document.write( "Question 935783: Find the inverse of the matrix
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Algebra.Com's Answer #569127 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

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Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix $\"A=%28matrix%282%2C2%2C1%2C1%2C4%2C4%29%29\"$ , we can follow these steps:

Step 1) Find the determinant

The determinant of $\"%28matrix%282%2C2%2C1%2C1%2C4%2C4%29%29\"$ is $\"abs%28matrix%282%2C2%2C1%2C1%2C4%2C4%29%29=0\"$ . So this means that $\"d=0\"$

Since the determinant is equal to zero, this means that no inverse exists.

Remember, the inverse of $\"%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\"$ is $\"%281%2Fd%29%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29\"$ .

If $\"d=0\"$ , then a division by zero occurs, which is NOT allowed.

So we can stop here.

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Answer:

So the inverse of $\"A=%28matrix%282%2C2%2C1%2C1%2C4%2C4%29%29\"$ does NOT exist since $\"d=0\"$ (ie the determinant is 0).

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