Question

if you were to solve the following system of equations by using a matrix which of the following would be your coefficient matrix? 4x-y=16 2x+3y=-18 A.(4 - 16) (2 -18) B. (4-1-16) (2 3 -18) C. (4 -1) ( 2 3) D. (4 2 ) (-1 3)

Answer 1

:)

Answer 2

When solving a system of equations using matrices, you want your coefficient matrix \[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\]to be such that\[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)\]gives you back your original equations. If we multiply this out we see that we get ax + by and cx + dy, so the coefficient matrix should then be either =\[\left[\begin{matrix}4 & -1 \\ 2 & 3\end{matrix}\right]\]or\[\left[\begin{matrix}2 & 3 \\ 4 & -1\end{matrix}\right]\]
Thus, C is the right answer.

Answer 3

By the way, I see where alchemista is coming from, but the solutions to the problem are put in a constant vector,; they are not part of the coefficient matrix.

Answer 4

Sorry the above is the augmented matrix, disregard my answer then

Answer 5

thanks!