Let A- -1- 2- 3 - and B- -2 -1 -4 -If trace of matrix AB is -12- then the value of k

The correct option is B 1 A=[ k; 2; 3 ] #160; B=[ 2 1 4 ] ∴ AB=[ 2k amp;k #160; amp;4k; 4 #160; amp; 2 #160; am ...

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Byju's Answer

Standard XII

Mathematics

Hermitian Matrix

Let A=[ -1;...

Question

Let $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦$ and $B = [\begin{matrix} - 2 & - 1 & - 4 \end{matrix}]$

If trace of matrix $A B$ is $- 12$ , then the value of $k$

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Solution

The correct option is B $1$
$A = ⎡ ⎢ ⎣ \begin{matrix} - k 23 \end{matrix} ⎤ ⎥ ⎦$

$B = [\begin{matrix} - 2 - 1 - 4 \end{matrix}]$

$∴ A B = ⎡ ⎢ ⎣ \begin{matrix} 2 k & k & 4 k - 4 & - 2 & - 8 - 6 & - 3 & - 12 \end{matrix} ⎤ ⎥ ⎦$

The trace (often abbreviated to tr) of a square matrix A is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A.

$∴ T r (A B) =$ Summation of diagonal elements $= 12$

$\Rightarrow + 2 k - 2 - 12 = - 12$ ...............(According to question)

$\Rightarrow 2 k = 14 - 12 = 2$

$\Rightarrow k = 1$

$∴ k = 1$

Hence, option B.

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Let A=⎡⎢⎣−123⎤⎥⎦ and B=[−2−1−4]If trace of matrix AB is −12, then the value of k

Let $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦$ and $B = [\begin{matrix} - 2 & - 1 & - 4 \end{matrix}]$

If trace of matrix $A B$ is $- 12$ , then the value of $k$