Solve the following system by elimination or substitution 2x

Solve the following system by elimination, or substitution. 2x - y = 4 x - 2y = -4 Given matrices A, B, C, and D: A = [2 -4 0 6 1 -5] B = [-1 9 0 5 8 7 2 4 0] C = [-5 8] D = [2 3 -3] (a) What is the size of matrices A, B, C, and D? (b) Find a_11, a_12, b_32, b_22, c_11, d_13 (c) Which of these matrices is a row matrix? (d) Which of these matrices is a square matrix? (e) For matrix A, find a_12 + a_23 + a_22 Perform the row operations indicated on the following matrix. Write the new matrix [1 -3 2 4 -6 -8]

Solution

1) 2x – y = 4 ………(1)

   x – 2y = -4 ………..(2)

Multiplying (1) by 2 and then subtracting (2) from (1),

4x – 2y = 8

   x - 2y = -4

=======> 3x = 12 ======> x = 4   and   y = 4

2) a) Matrix A is (2 x 3), Matrix B is (3 x 3), Matrix C is (2 x 1), and Matrix D is (1 x 3)

b)

c) Matrix D is row matrix

d) Matrix B is square matrix

e) All cofactors are zero in matrix A, so sum = 0