Question

A = (beginbmatrix 2 & 4 & 1 4 & 3 & x endbmatrix), B = (beginbmatrix -2 & 5 & 4 1 & 2y & 3 endbmatrix), A + B = C: (beginbmatrix 0 & 9 & 5 4 & 6 & 10 endbmatrix). If (x, y) is a solution to the equation and -1.

(A) The statement is incomplete.
(B) There is a contradiction in the equations.
(C) The solution is (x = 5, y = -2).
(D) The solution is (x = -1, y = 2)

Answer 1

To find the value of x and y in the equation A + B = C, we need to compare the corresponding components of the matrices A, B, and C. Let's compare the first and second rows of A + B with matrix C. The statement is incomplete.

Step-by-step explanation:

To find the value of x and y in the equation A + B = C, we need to compare the corresponding components of the matrices A, B, and C. Let's compare the first row: 2 + (-2) = 0, 4 + 5 = 9, and 1 + 4 = 5. These values match the first row of matrix C, so the first row of A + B is correct.

Now let's compare the second row: 4 + 1 = 5, 3 + (2y) = 6, and x + 3 = 10. Simplifying the equation 3 + (2y) = 6, we find that y = -1. Similarly, simplifying the equation x + 3 = 10, we find that x = 7. However, these values do not match the second row of matrix C, so the statement is incomplete. Therefore, the correct answer is (A) The statement is incomplete.