SOLUTION: Find the inverse of each matrix if it exists: (Top row) [3 7] (bottom row) [1 -4]

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Question 1129205: Find the inverse of each matrix if it exists:
(Top row) [3 7] (bottom row) [1 -4]
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Your matrix
matrix%282%2C2%2C3%2C7%2C1%2C-4%29
first make sure determinant is not zero
Δ = 3%2A%28-4%29-7%2A1
Δ =+-12-7
Δ = -19
so, determinant is not zero, therefore inverse matrix exists

Write the augmented matrix:
matrix%282%2C4%2C3%2C%097%2C%091%2C%090%2C%0D%0A1%2C%09-4%2C%090%2C%091%29

Find the pivot in the 1st column and swap the 2nd and the 1st rows:
matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A3%2C%097%2C%091%2C%090%29

Eliminate the 1st column:

matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%0919%2C%091%2C%09-3%29

Make the pivot in the 2nd column by dividing the 2nd row by 19:
matrix%282%2C4%2C1%2C%09-4%2C%090%2C%091%2C%0D%0A0%2C%091%2C%091%2F19%2C%09-3%2F19%29

Eliminate the 2nd column:


There is the inverse matrix on the right:

Eliminate the 2nd column:


Result:
matrix%282%2C2%2C%0D%0A4%2F19%2C7%2F19%2C%0D%0A1%2F19%2C-3%2F19%29