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In this question, we are asked to solve the following system of linear equations using the inverse matrix of the matrix of the coefficients of this system.
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Recall that to find the inverse matrix, we need to create the big augmented matrix whose left hand side contains the matrix of coefficients of this system.
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So it's going to be 5, 15, 56, negative 4, negative 11, negative 41.
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And the last row is going to be negative 1, negative 3, negative 11.
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And the right -hand side will contain the identity matrix.
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Now what we're going to do, we're going to reduce the matrix on the left -hand side to the identity matrix.
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And the matrix on the right hand side will be the required inverse.
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So the first step would be to interchange the first and the third rows.
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So we're going to get negative 1, negative 3, negative 11, negative 4, negative 11, negative 41, 5, 15, 56.
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Now don't forget to do the same on the right hand side.
01:47
We are going to get 0 -0 -1 0 -0 -0 -0 -0 -0 -0 -0.
01:57
Now let's multiply the first row by 4 by negative 4 and added to the second row.
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And multiply the first row by 5 and added to the last row.
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The first row will be same.
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Now the second row will become 0.
02:44
Negative 4 times negative 3 is going to be 12.
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12 minus 11 is going to be 1.
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Negative 4 times negative 11 is going to be 44.
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44 minus 41 is going to be 3.
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Now, negative 4, the right hand side will be 0, 1.
03:06
Negative 4 plus 0 is going to be negative 4.
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Now, let's see what happens to the last row.
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We are going to get 0.
03:16
Negative 3 times 5 is negative 15, plus 15 is going to be 0.
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5 times negative 11 is going to be negative 55, plus 56 is going to be 1.
03:28
Then it's going to be 1 0 5 plus 0 is going to be 5 now let's go in the reverse direction we're going to multiply the last row by negative 3 and added to the second row and we're going to multiply the last row by 11 and added to the first row we're going to get negative 1 negative 3 0 on the right hand side we're going to get 0 plus 11 is going to be 11 0 plus 0 is 0.
04:25
1 plus 55 is going to be 56.
04:31
In the second row we are going to get 0...