LetA- 1 0 0- 2 1 0- 3 2 1- -If u1 and u2 are column matrices such thatAu1- 1- 0- 0- - and Au2- 0- 1- 0- - then u1-u2 is equal to

Let u_1=[ a; b; c ] u_2=[ d; e; f ] Au_1=[ a; 2a+b; 3a+2b+c ]=[ 1; 0; 0 ] a=1, b= 2,c=1 u_1[ 1; 2; 1 ] Au_2=[ d; 2d+e; 3d+2e+f ]=[ 0; 1; ...

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Byju's Answer

Standard X

Mathematics

Null Matrix

LetA=[ 1 0 0;...

Question

Let
$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$
If $u_{1}$ and $u_{2}$ are column matrices such that
$A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦$ and $A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦$ , then $u_{1} + u_{2}$ is equal to

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

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

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

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

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Solution

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

Let $u_{1} = ⎡ ⎢ ⎣ \begin{matrix} a b c \end{matrix} ⎤ ⎥ ⎦ u_{2} = ⎡ ⎢ ⎣ \begin{matrix} d e f \end{matrix} ⎤ ⎥ ⎦$
$A u_{1} = ⎡ ⎢ ⎣ \begin{matrix} a 2 a + b 3 a + 2 b + c \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦$
$a = 1, b = - 2, c = 1$
$u_{1} ⎡ ⎢ ⎣ \begin{matrix} 1 - 2 1 \end{matrix} ⎤ ⎥ ⎦$
$A u_{2} = ⎡ ⎢ ⎣ \begin{matrix} d 2 d + e 3 d + 2 e + f \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦$
$u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 01 - 2 \end{matrix} ⎤ ⎥ ⎦$
$u_{1} + u_{2} = ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 - 1 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q.
Let A

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

.If

u_{1}

and

u_{2}

are column matrices such that

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

and

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

then

u_{1} + u_{2}

is equal to:

Q. Let

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

. If

u_{1}

and

u_{2}

are column matrices such that

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

and

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

then

u_{1} + u_{2}

is equal to

Q. For a matrix

A ⎛ ⎜ ⎝ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎞ ⎟ ⎠

, if

U_{1}, U_{2}

and

U_{3}

are

3 \times 1

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} ⎞ ⎟ ⎠

and

U

3 \times 3

matrix whose columns are

U_{1}, U_{2}

and

U_{3}

Then sum of the elements of

U^{- 1}

Let A = .

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

then u₁+u₂is equal to

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

and

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} ⎤ ⎥ ⎦

and

U

3 \times 3

matrix whose columns are

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

then answer the following question

The sum of elements of

U^{- 1}

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Let A=⎡⎢⎣100210321⎤⎥⎦ If u1 and u2 are column matrices such that Au1=⎡⎢⎣100⎤⎥⎦ and Au2=⎡⎢⎣010⎤⎥⎦, then u1+u2 is equal to