If A - begin bmatrix 28-3 1-4 - 1lend bmatrix - then adj3 A - 2-12 A is equal to51 - 84 163 - 72lendbmatrix B- 72 -8411-63 - 51lendbmatrix 72 -63 1-84 - 51lendbmatrix 51863 184 - 72lendbmatrix

The correct option is D [ 51 amp; 63; 84 amp; 72 ]We have, A = [ 2 amp; 3; 4 amp; 1 ] ∴ A^2 = A.A [ 2 amp; 3; 4 amp; 1 ] ...

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Standard IX

Mathematics

Adjoint of a Matrix

If A = begin ...

Question

If $A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}], then a d j (3 A^{2} + 12 A)$ is equal to

[\begin{matrix} 72 & - 84 - 63 & 51 \end{matrix}]

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[\begin{matrix} 51 & 63 84 & 72 \end{matrix}]

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[\begin{matrix} 51 & 84 63 & 72 \end{matrix}]

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[\begin{matrix} 72 & - 63 - 84 & 51 \end{matrix}]

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Solution

The correct option is B $[\begin{matrix} 51 & 63 84 & 72 \end{matrix}]$
We have, $A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}] ∴ A^{2} = A . A [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}] [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}] = [\begin{matrix} 4 + 12 & - 6 - 3 - 8 - 4 & 12 + 1 \end{matrix}] = [\begin{matrix} 16 & - 9 - 12 & 13 \end{matrix}] N o w, 3 A^{2} + 12 A = 3 [\begin{matrix} 16 & - 9 - 12 & 13 \end{matrix}] + 12 [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}] = [\begin{matrix} 48 & - 27 - 36 & 39 \end{matrix}] + [\begin{matrix} 24 & - 36 48 & 12 \end{matrix}] = [\begin{matrix} 72 & - 63 - 84 & 51 \end{matrix}] ∴ a d j (3 A^{2} + 12 A) = [\begin{matrix} 51 & 63 84 & 72 \end{matrix}]$

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Similar questions

Q. If

A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}], then a d j (3 A^{2} + 12 A)

is equal to

Find X and Y if

$(i i) 2 X + 3 Y = [\begin{matrix} 2 & 3 4 & 0 \end{matrix}] a n d 3 X + 2 Y = [\begin{matrix} 2 & - 2 - 1 & 5 \end{matrix}]$

If $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then verify that
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Q. If

A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}],

then adj

(3 A^{2} + 12 A)

is equal to:

Q. If

A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}]

, then adj

(3 A^{2} + 12 A)

is equal to.

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If A=[2−3−41], then adj(3A2+12A) is equal to

The correct option is B [51638472]We have, A=[2−3−41]∴A2=A.A[2−3−41] [2−3−41]=[4+12−6−3−8−412+1]=[16−9−1213]Now,3A2+12A=3[16−9−1213]+12[2−3−41]=[48−27−3639]+[24−364812]=[72−63−8451]∴adj(3A2+12A)=[51638472]

If $A = [\begin{matrix} 2 & - 3 - 4 & 1 \end{matrix}], then a d j (3 A^{2} + 12 A)$ is equal to