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Questions and Answers of College Algebra

Solve each problem using the Gauss-Jordan method to solve a system of equations.Three kinds of tea worth $4.60, $5.75, and $6.50 per lb are to be mixed to get 20 lb of tea worth $5.25 per lb. The
Use the Gauss-Jordan method to solve each system.2x - y + z = 4x + 2y - z = 03x + y - 2z = 1
Use the Gauss-Jordan method to solve each system.x - z = -3y + z = 62x - 3z = -9
Use the Gauss-Jordan method to solve each system.2x - y + 4z = -1-3x + 5y - z = 52x + 3y + 2z = 3
Use the Gauss-Jordan method to solve each system.3x + y = -7x - y = -5
Use the Gauss-Jordan method to solve each system.2x + 3y = 10-3x + y = 18
Use the Gauss-Jordan method to solve the system.5x + 2y = -103x - 5y = -6
Solve the system in terms of the specified arbitrary variable.2x - 6y + 4z = 55x + y - 3z = 1(z arbitrary)
Solve the system in terms of the specified arbitrary variable.3x - 4y + z = 22x + y = 1(x arbitrary)
Solve the problem using a system of equations.The equation of a circle may be written in the form x2 + y2 + ax + by + c = 0. Find the equation of the circle passing through the points (-3, -7), (4,
Solve the problem using a system of equations.The table was generated using a function y1 = ax2 + bx + c. Use any three points from the table to find the equation for y1. PLOAY UTR EN FARIAH
Solve the problem using a system of equations.In a study, a group of athletes was exercised to exhaustion. Let x represent an athlete’s heart rate 5 sec after stopping exercise and y this rate 10
Solve the problem using a system of equations.Let the supply and demand equations for units of backpacks be(a) Graph these equations on the same axes.(b) Find the equilibrium demand.(c) Find the
Solve the problem using a system of equations.The estimated resident populations (in percent) of young people (age 14 and under) and seniors (age 65 and over) in the United States for the years
Solve the problem using a system of equations.The Waputi Indians make woven blankets, rugs, and skirts. Each blanket requires 24 hr for spinning the yarn, 4 hr for dyeing the yarn, and 15 hr
Solve the problem using a system of equations.A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the
Solve the problem using a system of equations.A cup of uncooked rice contains 15 g of protein and 810 calories. A cup of uncooked soybeans contains 22.5 g of protein and 270 calories. How many cups
Solve each problem.Determine the system of equations illustrated in the graph. Write equations in standard form. y 2 3 -2,
Solve each problem.Create an inconsistent system of two equations.
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions,
Work the problem.What are the inverses of In, -A (in terms of A), and kA (k a scalar)?
Work the problem.Let Show that A3 = I3, and use this result to find the inverse of A. 0 0 -1 A = Lo 0 1 -1
Work the problem.Let where a, b, and c are nonzero real numbers. Find A-1. ь о Ь А —D| 0 A =
Work the problem.Suppose A and B are matrices, where A-1, B-1, and AB all exist. Show that (AB)-1 = B-1A-1.
Work the problem.Give an example of two matrices A and B, where (AB)-1 ≠ A-1B-1.
Work each problem.Prove that any square matrix has no more than one inverse.
Let and let O be the 2 × 2 zero matrix. Show that each statement is true.For square matrices A and B of the same dimension, if AB = O and if A-1 exists, then B = O. d
Let and let O be the 2 × 2 zero matrix. Show that each statement is true.A · O = O · A = O d
Use a graphing calculator and the method of matrix inverses to solve each system. Give as many decimal places as the calculator shows. пх + ey + V2— 1 ex + пу + V2; — 2 /2x 2z = V2r + ey +
Use a graphing calculator and the method of matrix inverses to solve each system. Give as many decimal places as the calculator shows.(log 2)x + (ln 3)y + (ln 4)z = 1(ln 3)x + (log 2)y + (ln 8)z =
Use a graphing calculator and the method of matrix inverses to solve each system. Give as many decimal places as the calculator shows. x - V2y = 2.6 y = -7 0.75x +
Use a graphing calculator and the method of matrix inverses to solve each system. Give as many decimal places as the calculator shows. 2.1х + у%3D V5 VZх - 2у %3D 5
Use a graphing calculator to find the inverse of each matrix. Give as many decimal places as the calculator shows. 1.4 0.5 0.59 0.84 1.36 0.62 [0.56 0.56 0.47 1.3
Use a graphing calculator to find the inverse of each matrix. Give as many decimal places as the calculator shows. 4 2 3 -/2 -/-
Use a graphing calculator to find the inverse of each matrix. Give as many decimal places as the calculator shows. V2 0.5 -17
Use a graphing calculator to find the inverse of each matrix. Give as many decimal places as the calculator shows. 0.7 V3 22
The number of automobile tire sales is dependent on several variables. In one study the relationship among annual tire sales S (in thousands of dollars), automobile registrations R (in millions), and
The amount of plate-glass sales S (in millions of dollars) can be affected by the number of new building contracts B issued (in millions) and automobiles A produced (in millions). A plate-glass
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.x - 2y + 3z = 1y - z + w = -1-2x + 2y - 2z + 4w = 22y - 3z + w = -3
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.x + y + 2w = 32x - y + z - w = 33x + 3y + 2z - 2w = 5x + 2y + z = 3
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.2x + 4y + 6z = 4-x - 4y - 3z = 8y - z = -4
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.2x + 2y - 4z = 122x + 6y = 16-3x - 3y + 5z = -20
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.-2x + 2y + 4z = 3-3x + 4y + 5z = 1x + 2z = 2
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.2x + 3y + 3z = 1x + 4y + 3z = 0x + 3y + 4z = -1
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.2x + 5y + 2z = 94x - 7y - 3z = 73x - 8y - 2z = 9
Solve each system by using the inverse of the coefficient matrix. For Exercises , the inverses were found in Exercises.x + y + z = 62x + 3y - z = 73x - y - z = 6
Show that the matrix inverse method cannot be used to solve each system.x - 2y + 3z = 42x - 4y + 6z = 83x - 6y + 9z = 14
Show that the matrix inverse method cannot be used to solve each system.7x - 2y = 314x - 4y = 1
Solve each system using the inverse of the coefficient matrix. 12 5 10 3
Solve each system using the inverse of the coefficient matrix. 49 x +-y = 18 x- 3 4 x + 2y 3
Solve each system using the inverse of the coefficient matrix.0.5x + 0.2y = 0.80.3x - 0.1y = 0.7
Solve each system using the inverse of the coefficient matrix.0.2x + 0.3y = -1.90.7x - 0.2y = 4.6
Solve the system using the inverse of the coefficient matrix.5x - 3y = 010x + 6y = -4
Solve the system using the inverse of the coefficient matrix.6x + 9y = 3-8x + 3y = 6
Solve the system using the inverse of the coefficient matrix.2x - 3y = 102x + 2y = 5
Solve the system using the inverse of the coefficient matrix.3x + 4y = -3-5x + 8y = 16
Solve the system using the inverse of the coefficient matrix.x + 3y = -122x - y = 11
Solve the system using the inverse of the coefficient matrix.2x - y = -83x + y = -2
Solve the system using the inverse of the coefficient matrix.x + y = 5x - y = -1
Solve the system using the inverse of the coefficient matrix.-x + y = 12x - y = 1
Each graphing calculator screen shows A-1 for some matrix A. Find each matrix A.
Find the inverse, if it exists, for the matrix. 2 -1 2 -1 -1 2.
Find the inverse, if it exists, for the matrix. 3 0 -2 -1 -2 2 -2 4 2 -3 1.
Find the inverse, if it exists, for the matrix. -1 3 3 2 -2 2 1 0 2.
Find the inverse, if it exists, for the matrix. -1 -4 -3 0 1 -1.
Find the inverse, if it exists, for the matrix. 2 -4 2 5] -3 -3 2.
Find the inverse, if it exists, for the matrix. -2 2 4 -3 4 5 1 0 2.
Find the inverse, if it exists, for the matrix. 2 3 3 1 4 4 3 3 4
Find the inverse, if it exists, for the matrix. -1
Find the inverse, if it exists, for the matrix. -1 [2
Find the inverse, if it exists, for the matrix. -6 4 -3 2.
Find the inverse, if it exists, for the matrix. 10 -3 -6]
Find the inverse, if it exists, for the matrix. 3 -1 2] -5
Find the inverse, if it exists, for the matrix. -2 -1 3 4.
Find the inverse, if it exists, for each matrix. -1 [2
Find the inverse, if it exists, for each matrix. -2 -1
Decide whether or not the given matrices are inverses of each other. 3 and -3 -3 3 -1 3 4 3.
Decide whether or not the given matrices are inverses of each other. 0| and 0 -1 0 -1 1 -1
Decide whether or not the given matrices are inverses of each other. -2 0 2 0 and 0 1. -1
Decide whether or not the given matrices are inverses of each other. 0. 0 -2| and |1 -1 -1
Decide whether or not the given matrices are inverses of each other. [2 2 1 and [3 2] 2 -3 2.
Decide whether or not the given matrices are inverses of each other. -2 -5 -1 and -3 3 -5 3 -1
Decide whether or not the given matrices are inverses of each other. -1 3 3 and 3 -2.
Decide whether or not the given matrices are inverses of each other. [5 7 [2 3] 3 -7 and 3 5. -2
Let Show that AI2 = I2 A = A, thus proving that I2 is the identity element for matrix multiplication for 2 × 2 square matrices. b' and I2 ||
Show that I3 A = A for ¯i 0 07 -2 4 and I3 9. 3 5 13 =| 0 1 0 8 -6
What is the matrix equation form of the following system?6x + 3y = 95x - y = 4Provide a proof for each of the following.
Answer the question.What is the coefficient matrix of the following system?3x - 6y = 8-x + 3y = 4
Answer the question.It can be shown that the following matrices are inverses. What is their product (in either order)? 0 -1 0 and 0 -1 0 -1

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