how do i find the inverse of the matrix
[ 10 9 ]
[ 8 -1 ]
Please learn to spell A L G E B R A.
im having trouble with this problem
6( n - 4 ) = 3n
To find the inverse of a matrix, you can follow these steps:
Step 1: Write down the given matrix:
[ 10 9 ]
[ 8 -1 ]
Step 2: Calculate the determinant of the matrix. The determinant of a 2x2 matrix [a b; c d] is calculated as (ad - bc). For our given matrix, the determinant is (10 * (-1) - 9 * 8) = (-10 - 72) = -82.
Step 3: Check if the matrix is invertible. A matrix is invertible (i.e., its inverse exists) only if its determinant is not equal to zero. In this case, since the determinant (-82) is not equal to zero, the matrix is invertible.
Step 4: Swap the diagonal elements (10 and -1) and change the sign of the other two elements:
[ -1 9 ]
[ 8 10 ]
Step 5: Divide each element of the matrix by the determinant (-82):
[ -1/-82 9/-82 ]
[ 8/-82 10/-82 ]
Simplifying the fractions gives:
[ 1/82 -9/82 ]
[ -8/82 -10/82 ]
So, the inverse of the given matrix is:
[ 1/82 -9/82 ]
[ -8/82 -10/82 ]