Question

find the reverse operation that transforms the second matrix into the first. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

The reverse operation that transforms the second matrix into the first is called the inverse operation. In matrix algebra, the inverse of a matrix A is denoted as A^-1 and it has the property that when multiplied by the original matrix A, the result is the identity matrix, denoted as I.

Step-by-step explanation:

The reverse operation that transforms the second matrix into the first is called the inverse operation. In matrix algebra, the inverse of a matrix A is denoted as A-1 and it has the property that when multiplied by the original matrix A, the result is the identity matrix, denoted as I. In other words, if A is a matrix and A-1 is its inverse, then A x A-1 = I.

To find the inverse of a matrix, you can use the following steps:

1. Calculate the determinant of the matrix A. If the determinant is zero, the matrix does not have an inverse.
2. Find the adjugate of matrix A by taking the transpose of its cofactor matrix. The cofactor of each element is calculated by finding the determinant of the submatrix formed by deleting the row and column containing that element.
3. Divide the adjugate of A by the determinant of A to obtain the inverse matrix A-1.

For example, let's say we have two matrices:

A = [[2, 3], [4, 5]]

B = [[5, -3], [4, 2]]

If B is the inverse of A, then A x B = I:

[[2, 3], [4, 5]] x [[5, -3], [4, 2]] = [[1, 0], [0, 1]]