Evaluate 3- 1 amp-1- -2 amp-0- 1 amp- -2 - -5 amp- 2- -1 amp-3- 4 amp-4 - 8 amp- 5- 5 amp-3- 1 amp- 2 - 8 amp- -5- -5 amp-3- -1 amp- -2 - 8 amp- -5- 7 amp-4- 1 amp- 2 - 2 amp- 1- 5 amp-3- -1 amp- -2 -

The correct option is B [ 8 amp; 5; 5 amp; 3; 1 amp; 2 ] 3[ 1 amp; 1; 2 amp;0; 1 amp; 2 ]=[ 3 amp; 3; 6 a ...

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Byju's Answer

Standard X

Mathematics

Scalar Multiplication of a Matrix

Evaluate 3[ ...

Question

Evaluate $3 ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 - 2 & 0 1 & - 2 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 5 & 2 - 1 & 3 4 & - 4 \end{matrix} ⎤ ⎥ ⎦$

$⎡ ⎢ ⎣ \begin{matrix} 8 & - 5 7 & 4 1 & 2 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 5 & 3 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 8 & 5 5 & 3 1 & 2 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 8 & - 5 - 5 & - 3 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is D
$⎡ ⎢ ⎣ \begin{matrix} 8 & - 5 - 5 & - 3 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$

$3 ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 - 2 & 0 1 & - 2 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 3 - 6 & 0 3 & - 6 \end{matrix} ⎤ ⎥ ⎦$

$⎡ ⎢ ⎣ \begin{matrix} 3 & - 3 - 6 & 0 3 & - 6 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 5 & 2 - 1 & 3 4 & - 4 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 8 & - 5 - 5 & - 3 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$

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Find x, if

$(i) {(\frac{1}{4})}^{- 4} \times {(\frac{1}{4})}^{- 8} = {(\frac{1}{4})}^{- 4 x} (i i) {(\frac{- 1}{2})}^{- 19} \div {(\frac{- 1}{2})}^{8} = {(\frac{- 1}{2})}^{- 2 x + 1} (i i i) {(\frac{3}{2})}^{- 3} \div {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 x + 1} (i v) {(\frac{2}{5})}^{- 3} \times {(\frac{2}{5})}^{15} = {(\frac{2}{5})}^{2 + 3 x} (v) {(\frac{5}{4})}^{- x} \div {(\frac{5}{4})}^{- 4} = {(\frac{5}{4})}^{5} (v i) {(\frac{8}{3})}^{2 x + 1} \times {(\frac{8}{3})}^{5} = {(\frac{8}{3})}^{x + 2}$

Q. Evaluate:
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\frac{8^{- 1} \times 5^{3}}{2^{- 4}}

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(5^{- 1} \times 2^{- 1}) \times 6^{- 1}

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$\frac{8^{- 1} \times 5^{3}}{2^{- 4}}$

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Evaluate 3⎡⎢⎣1−1−201−2⎤⎥⎦−⎡⎢⎣−52−134−4⎤⎥⎦

The correct option is D ⎡⎢⎣8−5−5−3−1−2⎤⎥⎦ 3⎡⎢⎣1−1−201−2⎤⎥⎦=⎡⎢⎣3−3−603−6⎤⎥⎦ ⎡⎢⎣3−3−603−6⎤⎥⎦−⎡⎢⎣−52−134−4⎤⎥⎦=⎡⎢⎣8−5−5−3−1−2⎤⎥⎦

Evaluate $3 ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 - 2 & 0 1 & - 2 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 5 & 2 - 1 & 3 4 & - 4 \end{matrix} ⎤ ⎥ ⎦$