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Transpose of a Matrix

Let A=[ 1 0 0...

Question

Let A = .

If u₁ and u₂ are column matrices such that Au₁= and Au₂= ,

then u₁+u₂is equal to

A

$⎡ ⎢ ⎣ \begin{matrix} - 1 10 \end{matrix} ⎤ ⎥ ⎦$

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B

$⎡ ⎢ ⎣ \begin{matrix} - 1 1 - 1 \end{matrix} ⎤ ⎥ ⎦$

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C

$⎡ ⎢ ⎣ \begin{matrix} - 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦$

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D

$⎡ ⎢ ⎣ \begin{matrix} 1 - 1 - 1 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is D
$⎡ ⎢ ⎣ \begin{matrix} 1 - 1 - 1 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

= ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦

u_{1}

u_{2}

are column matrices such that

A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦

A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦

u_{1} + u_{2}

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

u_{1}

u_{2}

are column matrices such that

A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦

A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦

u_{1} + u_{2}

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

u_{1}

u_{2}

are column matrices such that

A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦

A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦

u_{1} + u_{2}

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦, U_{1}, U_{2}

U_{3}

are columns matrices satisfying

A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦

U

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

then answer the following question

| U |

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

U_{1}, U_{2}, U_{3}

be column
matrices satisfying

A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦, A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦

3 \times 3

matrix whose columns are

U_{1}, U_{2}, U_{3}

| U | =

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