SOLUTION: The inverse of A= 13 -4 is 3 1

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Question 1133440: The inverse of A= 13 -4 is
3 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A=matrix%282%2C2%2C+13+%2C-4+%2C3%2C1%29

Determinant is not zero, therefore inverse matrix exists:

Write the augmented matrix

matrix%282%2C4%2C13%2C-4%2C1%2C%090%2C%0D%0A3%2C%091%2C%090%2C%091%29

Make the pivot in the 1st column by dividing the 1st row by 13


matrix%282%2C4%2C1%2C-4%2F13%2C1%2F13%2C%090%2C%0D%0A3%2C%091%2C%090%2C%091%29


Eliminate the 1st column




Make the pivot in the 2nd column by dividing the 2nd row by 25%2F13





Eliminate the 2nd column



There is the inverse matrix on the right



Result:

matrix%282%2C2%2C1%2F25%2C%094%2F25%2C%0D%0A-3%2F25%2C%0913%2F25%29

factor out 1%2F25

A%5E-1=%281%2F25%29%28matrix%282%2C2%2C1%2C4%2C-3%2C13%29%29