Consider the following LU decomposition of the given matrix: 2 1 -1 2 1 0 OT2 1 -1 2 0 a22 U23 U24 оо азз И34 4 5 -3 6 21 1 -2 5 -2 6 131 /32 1 4 11 -4 8 41 42 l43 1 0 0 O a44 What is I32? none of the choices 2 -2

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A: a symmetric matrix is a square matrix that is equal to its transpose.

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A: The answer is in below steps.

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A: Let us find the basis for the null space of A in the next steps.

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A: To compute the following matrix

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A: First of all, consider the given equation for matrices multiplication.

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A: We will give a counter example that will prove this statement wrong.

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A: Let A=1022-13418. To obtain the LU-decomposition matrix, use the elementary transformation.…