Final answer:
To find the inverse of the matrix, calculate the determinant, find the adjugate, and multiply it by 1/det(A).
Step-by-step explanation:
The inverse of a matrix is denoted as A-1. To find the inverse of a matrix, you can use the formula A-1 = (1/det(A)) * adj(A), where det(A) is the determinant of the matrix and adj(A) is its adjugate. First, calculate the determinant of the matrix:
|5 7 4|
|3 -13 0|
|6 7 5|
Determinant = 5*(-13)*5 + 7*0*6 + 4*7*3 - 4*(-13)*6 - 7*7*5 - 5*0*3 = -287.
Next, find the adjugate of the matrix:
|(-5) -4 -8|
|(-35) 25 43|
|(-28) 21 33|
Finally, multiply the adjugate by 1/det(A):
A-1 = (1/(-287)) * |(-5) -4 -8|
|(-35) 25 43|
|(-28) 21 33|
So, the inverse of the given matrix is:
|(-5)/(-287) -4/(-287) -8/(-287)|
|(-35)/(-287) 25/(-287) 43/(-287)|
|(-28)/(-287) 21/(-287) 33/(-287)|