Compute the products AB and BA whichever exists in each of the followi

1.	Compute the products AB and BA whichever exists in each of the following cases :[a,b] \(\begin{bmatrix} c \\[0.3em] d \\[0.3em] \end{bmatrix}\) + [a b c d] \(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\)
Answer» [a,b] \(\begin{bmatrix} c \\[0.3em] d \\[0.3em] \end{bmatrix}\) + [a b c d] \(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\) = [ ac + bd] + [a² + b² + c² + d²] = [ ac + bd = a²+ b² + c² + d²] Hence, [a b] \(\begin{bmatrix} c \\[0.3em] d \end{bmatrix}\) + [ a b c d]\(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\) = [ ac + bd = a²+ b² + c² + d²]

Compute the products AB and BA whichever exists in each of the following cases :[a,b] \(\begin{bmatrix} c \\[0.3em] d \\[0.3em] \end{bmatrix}\) + [a b c d] \(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\)

Answer»

[a,b] \(\begin{bmatrix} c \\[0.3em] d \\[0.3em] \end{bmatrix}\) + [a b c d] \(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\)

= [ ac + bd] + [a² + b² + c² + d²]

= [ ac + bd = a²+ b² + c² + d²]

Hence,

[a b] \(\begin{bmatrix} c \\[0.3em] d \end{bmatrix}\) + [ a b c d]\(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\)

= [ ac + bd = a²+ b² + c² + d²]

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Compute the products AB and BA whichever exists in each of the following cases :[a,b] \(\begin{bmatrix} c \\[0.3em] d \\[0.3em] \end{bmatrix}\) + [a b c d] \(\begin{bmatrix} a \\[0.3em] b \\[0.3em] c \\[0.3em] d \end{bmatrix}\)

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