If AT- 3 4- -1 2- 0 1 - and B- -1 2 1- 1 2 3- -then find AT-BT

If A^T=[ 3 amp;4; nbsp; 1 amp; 2; nbsp; 0 amp;1 nbsp; ] and B=[ 1 amp;2 amp;1; nbsp; 1 amp;2 amp;3; nbsp; ] B^T=[ 1 ...

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Properties of Matrix Multiplication

If AT=[ 3 4; ...

Question

If $A^{T} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦ and B = [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}]$ ,

then find $A^{T} - B^{T}$

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Solution

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A^{T} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦

B = [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}]

A^{T} - B^{T} .

A^{T} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦

B = [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}]

A^{T} - B^{T}

If and, then verify that

(i)

(ii)

A^{T} = [\begin{matrix} 3 & 4 \\ - 1 & 2 \\ 0 & 1 \end{matrix}] and B = [\begin{matrix} - 1 & 2 & 1 \\ 1 & 2 & 3 \end{matrix}]

A = ⎡ ⎢ ⎣ \begin{matrix} - 1 5 - 2 \end{matrix} \begin{matrix} 271 \end{matrix} \begin{matrix} 391 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} - 4 11 \end{matrix} \begin{matrix} 123 \end{matrix} \begin{matrix} - 5 01 \end{matrix} ⎤ ⎥ ⎦

(i) {(A + B)}^{T} = A^{T} + B^{T}

(i i) {(A - B)}^{T} = A^{T} - B^{T}

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