Compute the following: begin{bmatrix} a^2 + b | vedclass

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(A) To compute the sum of the two matrices,we add the corresponding elements of each matrix: $\begin{bmatrix} a^2 + b^2 & b^2 + c^2 \ a^2 + c^2 & a^2

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$\begin{bmatrix} (a+b)^2 & (b+c)^2 \ (a-c)^2 & (a-b)^2 \end{bmatrix}$

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(A) To compute the sum of the two matrices,we add the corresponding elements of each matrix: $\begin{bmatrix} a^2 + b^2 & b^2 + c^2 \ a^2 + c^2 & a^2 + b^2 \end{bmatrix} + \begin{bmatrix} 2ab & 2bc \ -2ac & -2ab \end{bmatrix}$ $= \begin{bmatrix} a^2 + b^2 + 2ab & b^2 + c^2 + 2bc \ a^2 + c^2 - 2ac & a^2 + b^2 - 2ab \end{bmatrix}$ Using the algebraic identities $(x+y)^2 = x^2 + y^2 + 2xy$ and $(x-y)^2 = x^2 + y^2 - 2xy$,we get: $= \begin{bmatrix} (a+b)^2 & (b+c)^2 \ (a-c)^2 & (a-b)^2 \end{bmatrix}$

Compute the following: $\begin{bmatrix} a^2 + b^2 & b^2 + c^2 \\ a^2 + c^2 & a^2 + b^2 \end{bmatrix} + \begin{bmatrix} 2ab & 2bc \\ -2ac & -2ab \end{bmatrix}$

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