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mathematics
precalculus

Questions and Answers of Precalculus

Matrix is nonsingular. Find the inverse of each matrix. 2
Find the product. 4 -2 3 2 -1 -1
Find the product. [1 3 2 4 1 2 3 6 1 -1
Find the product. -1 2 8 -1 -3 3 6 5
Find the product. 2 3 0 -1 4 2 4
Find the product. 4 1 -6 6 1 0 2 2 1 2 5 4 -1 4
Find the product. 1 4 6 2 -2 0 || 3 -1 3 2
Use the following matrices to evaluate the given expression. AC + BC 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. CA - CB 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. CA – 5I3 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. AC – 3I2 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. (A + B)C 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. C(A + B) 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. CB 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. CA 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. BC 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. AC 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. 2A + 4B 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. 3A - 2B 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. -3B 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. 4A 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. A - B 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
Use the following matrices to evaluate the given expression. A + B 4 0 3 -5 4 1 -[:] 6. 6 2 -2 -2 B = -2 3 -2 3 -2
If X represents a matrix equation where A is a nonsingular matrix, then we can solve the equation using X = _______.
True or False The identity matrix has properties similar to those of the real number 1.
If a matrix A has no inverse, it is called _______.
Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB = BA = In is called the _______ of the matrix A.
True or False.Matrix multiplication is commutative.
Find the product AB of two matrices A and B, the number of ________ in matrix A must equal the number of ________ in matrix B.
True or False.Matrix addition is commutative.
A matrix that has the same number of rows as columns is called a(n) ________ matrix.
Prove that, if row 2 of a 3 by 3 determinant is multiplied by k, k ≠0 and the result is added to the entries in row 1, there is no change in the value of the determinant.
Prove that a 3 by 3 determinant in which the entries in column 1 equal those in column 3 has the value 0.
Multiply each entry in row 2 of a 3 by 3 determinant by the number k, k ≠0. Show that the value of the new determinant is k times the value of the original determinant.
Interchange columns 1 and 3 of a 3 by 3 determinant. Show that the value of the new determinant is times the value of the original determinant.
Complete the proof of Cramer’s Rule for two equations containing two variables.
Show that х 1 y 1 (у — г)(х — у)(х — г) .2 |I
A triangle has vertices (x1, y1), (x2 , y2) and (x3, y3). The area of the triangle is given by the absolute value of D, where Use this formula to find the area of a triangle with vertices (2,
Using the result obtained in Problem 57, show that three distinct points (x1, y1), (x2 , y2) and (x3, y3) are collinear (lie on the same line) if and only if Х1 У1 1 Х2 У2 1 3 0 |Хз Уз 1
An equation of the line containing the two points (x1, y1) and (x2 , y2)may be expressed as the determinantProve this result by expanding the determinant and comparing the result to
Solve for x. -4x 3 х |0 1 2
Solve for x. 2 3 1 -2 6.
Solve for x. 3 4 |1 | -2
Solve for x. * 1 4 3 2 -1 2 1 = 2
Solve for x. 1 -2 . 3
Solve for x. = 5 4 3
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 x + 3 y + 6 z + 9 3u – 1 3v – 2 3w – 3 |3и -1 3v- Зw 3
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 2 2y и — 1 v — 2 w 2х 2z 3 3.
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 x y z - x Z. v w – u 2.
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 1 2 3 3 y – 6 2u 2v 2w
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 2 3 |x — и у — v z— w и
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 y | -3 -6 -9 и
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 х у и и 2 4 6.
Use properties of determinants to find the value of each determinant if it is known that х у w = 4 и 1 2 3 3 и х у
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х — у + 2z %3 0 Зх + 2у 3D 0 — — 4z %3D 0 —2х + 2у
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х — 2у + 3г %3D 0 Зх + у — 2z %3D0 2х — 4у + 62 %3D0
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х+ 4у — 3z %3D 0 Зх — у+ 3z 3D 0 х+ у+ 6z %3D 0
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. x + 2y – z = 0 2x – 4y + z = 0 -2x + 2y – 3z = 0
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 5 x - y + 2z = 4 Зх + 2y -2x + 2y – 4z = - 10
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х — 2у + 3z %3D 1 Зх + у — 2z %3D 0 2х — 4y + 6z 3D 2
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. — 3z %3D —8 Зх — у + 3z %3D 12 х+ у+ 6z х + 4у 1.
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. x + 2y – z = -3 2x – 4y + z = -7 -2x + 2y – 3z = 4
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х — y + z = -4 2х — Зу + 4z%3D —15 5х + у — 2z %3D 12 -15
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. x + y - z = 6 3x – 2y + z = -5 x + 3y – 2z = 14
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 2х — у 3D —1 3 х + 2 2 ||
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. | 3х — 5у 3D3 15х + 5у —D 21
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. -х + у %3D —2 х — 2у 3D 8
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 3D 6 2х + Зу y = х-
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. Зx 2y = 0 I| 5х + 10у 3D 4
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 2х — Зу %3D —1 10х + 10у %3 5 Dy
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. Зх + Зу — 3 8. 4х + 2у %3D 3
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 4y 2х — 4y %3D -2 Зх + 2y 3 ||
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. J-x + 2y = 5 4х — 8y — 6
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. Зх — 2у 3 4 |6х — 4у 3D 0
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 2х + 4y 3D 16 Зх — 5у 3D —9 ||
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. Зх — бу 3 24 5х + 4y — 12 ||
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. S -2y = -4 4x + 5y = –3
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. Зх 3D 24 х+ 2у %3D 0
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. х + 3у 3D 5 2х — Зу %3D —8 5
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 5х y = 13 %3D 2х + Зу 3D 12
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. fx + х + 2у %3D 5 lx - y = 3
Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. |x + y = 8 = 4 х
Find the value of each determinant. 3 -9 4 4 0 8 -3 1
Find the value of each determinant. -1 2 4 -1 0 -3 4 6.
Find the value of each determinant. |1 3 -2 1 -5 6 1 2 3|
Find the value of each determinant. 4 2 -1 5 -2|
Find the value of each determinant. -4 2 -5 3
Find the value of each determinant. -3 -1 4 2.
Find the value of each determinant. 8 -3 4 2.
Find the value of each determinant. 6 4 -1 3
True or False.If any row (or any column) of a determinant is multiplied by a nonzero number k, the value of the determinant remains unchanged.
True or False.The value of a determinant remains unchanged if any two rows or any two columns are interchanged.
True or False. When using Cramer’s Rule, if , then the system of linear equations is inconsistent.
True or False.A determinant can never equal 0.
Using Cramer’s Rule,the value of x that satisfies the system of equations S2x + 3y = 5 lx - 4y = -3 is x |2 |1 -4| 3.
A doctor’s prescription calls for the creation of pills that contain 12 units of vitamin and 12 units of vitamin E. Your pharmacy stocks three powders that can be used to make these pills: one
Write a brief paragraph or two that outline your strategy for solving a system of linear equations using matrices.
A doctor’s prescription calls for a daily intake of a supplement containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks three supplements that can be used: one
A young couple has $25,000 to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money in corporate bonds that yield 9%, and some
Three retired couples each require an additional annual income of $2000 per year.As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money

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