Question

Find the inverse matrix or type "none". [[-1,2],[2,-3]]

Answer 1

To find the inverse matrix, we need to set up the given matrix and follow these steps: find the determinant, check if the determinant is not zero, find the adjugate matrix, and multiply the adjugate matrix by the reciprocal of the determinant. In this case, the inverse matrix of [[-1,2],[2,-3]] is [[1/9, 2/9],[-2/9, 1/9]].

Step-by-step explanation:

To find the inverse of a matrix, we need to follow these steps:

1. Set up the matrix with the given values.
2. Find the determinant of the matrix.
3. If the determinant is not equal to zero, find the adjugate matrix.
4. Multiply the adjugate matrix by the reciprocal of the determinant to get the inverse matrix.

In this case, the given matrix is [[-1,2],[2,-3]].

Step 1: Set up the matrix.

| -1 2 |

| 2 -3 |

Step 2: Find the determinant.

Determinant = (-1)(-3) - (2)(2) = -5 - 4 = -9

Step 3: Check if the determinant is not zero.

-9 is not equal to zero, so we can continue to the next step.

Step 4: Find the adjugate matrix.

Adjugate Matrix = [[-3,-2], [2,-1]]

Step 5: Multiply the adjugate matrix by the reciprocal of the determinant.

Inverse Matrix = (1/-9) * [[-3,-2], [2,-1]]

= [[1/9, 2/9],[ -2/9, 1/9]]