Question

30 Points!!

Juan solves the system of equations by forming a matrix equation.

−4x+y=9
3x+2y=7

He multiplies the left side of the coefficient matrix by the inverse matrix.

How does he proceed to the solution?

Answer 1

I used the above answer and got it wrong. Hope this helps! (Sorry it looks a little weird... just look at whta is in the boxes)

Explanation:

Answer 2

multiply the left side of the constant vector by the inverse matrix

Explanation:

The matrix equation ...

AX = B

is solved by left-multiplying by the inverse of A:

A⁻¹AX = A⁻¹B

IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix

X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix

`\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^(-1)\left[\begin{array}{c}9&7\end{array}\right]=(1)/(11)\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right]`