00:01
In this question, we are given the following equation involving a block matrices and we're asked to find, where we're also given that c11 is invertible.
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And we're asked to find x, y and d222.
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Basically, a block matrix multiplication works in the same way as usual number matrix multiplication, assuming that all blocks are compatible here.
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Therefore, we will just multiply the matrices on the left.
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So i 0 times the first column of matrix c is going to give us i times c11 and since i is the identity matrix it's just going to be c11.
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Now first row times second column is going to give us i times c12 which is simply going to be c12.
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Next we're going to multiply the second row by the first column.
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We're going to get y times c11 plus i.
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I times c to 1 it's going to be just c to 1 i should leave more space here now let's multiply the second row by the second column we're going to get y times c1 2 plus i times c2 finally let's multiply the last column by the last row by the first column we're going to get x times c11 plus c3 1 and for the last entry we're going to going to multiply we're going to get x times c12 plus c32 and all this must be equal to the matrix d1d1 2 0 d2 and 0 d32 now by comparing entries we see that y times c11 plus c2 is equal to 0 because the corresponding entry on the right hand side is equal to 0...