3.1 Systems of Two Linear Equations in Two Variables A. Solve the system by graphing (by hand or with Excel) 3x +5y = 46 7x - y = 6 B. Solve the system by graphing (by hand or with Excel) 4x - 5y = 7 2x + 3y = 9 3.2 Matrices and Linear Equations in Two Variables C. Find the dimensions of the matrix and the values of a2,1 and a3,1 5 9 1 2 3 6 12 4 2 7 3 8 D. Find the dimensions of the matrix and the values of a1,3 and a2,3 7 5 3 4 9 1 14 2 8 6 9 10 E. Write the augmented matrix representing the system of linear equations. 5 x 7 y 2 2x y 3 F. Write the augmented matrix representing the system of linear equations. 3x 5 y 8 4x y 5 G. Carry out the row operation: 1 12 32 1 R2 R2 2 0 2 16 H. Carry out the row operation: 8 24 32 1 R1 R1 8 5 22 16 I. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as inconsistent or dependent. 1 0 9 0 1 15 J. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as inconsistent or dependent. 1 0 157 0 1 386 K. Solve the system by row-reducing the corresponding augmented matrix. x 2 y 12 3x y 11 3.3 Systems of Linear Equations and the Gauss-Jordan Method L. Find the augmented matrix representing the system of equations: x1 2 x2 x3 2 3x1 x2 4 x3 6 x 3x x 1 2 1 M. Interpret the row-reduced matrix as the solution of a system of equations: 1 0 0 5 0 1 0 9 0 0 1 2 N. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix: 1 0 1 15 0 1 0 9 0 0 1 2 O. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix: 1 0 0 7 0 1 0 16 0 0 2 32 3.4 Matrix Arithmetic For problems P - U, use matrices A, B, and C below. 2 3 4 A 5 6 7 8 9 1 8 7 6 B 5 4 3 2 1 9 1 6 5 C 7 2 8 4 9 3 At 2B -3C B+C C-A A + 2B P. Q. R. S. T. U. Find: Find: Find: Find: Find: Find: V. Find the matrix product: 2 2 3 1 1 3 1 3 2 W. Find the matrix product: 2 2 2 3 1 1 4 3 1 3 3 3 X. Find the matrix product: 2 4 5 2 3 1 1 3 2 Y. Rewrite the system of linear equations as a matrix equation AX = B 2 x1 3x2 4 x3 1 5 x1 8 x2 6 x3 3 2 x 3x 3 x 8 2 3 1 Z. Rewrite the system of linear equations as a matrix equation AX = B 2 x1 3 x2 4 x3 5 x4 6 5 x1 8 x2 6 x3 4 x4 1 2 x 3x 3 x 6 x 14 2 3 4 1