Let M be a 3 - 3 matrix satisying M -eginbmatrix 0 11 W0lend bmatrix - begin bmatrix 2113endbmatrix - 11 Mbmatrix 1110lendbmatrix -lbeginbmatrix 111111-1lendbmatrix - 11 and - M -eginbmatrix 1111111lendbmatrix - beginbmatrix 0 10 l12

The correct option is D 9Let M = nbsp;[ a_1 amp; a_2 amp;a_3; nbsp; b_1 amp; b_2 amp; b_3; nbsp; c_1 amp; c_2 amp; c_3 ] ∴ M [ 0; 1; 0 ] = [ 1; ...

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Multiplication of Matrices

Let M be a 3 ...

Question

Let M be a $3 \times 3$ matrix satisying $M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .$
Then, find the sum of the diagonal entries of M.

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3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .

3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .

If A = [\begin{matrix} 3 & - 1 4 & - 1 \end{matrix}] and A^{10} = [\begin{matrix} a_{11} & a_{12} a_{21} & a_{22} \end{matrix}], then a_{11} + a_{22} =

m [\begin{matrix} - 3 & 4 \end{matrix}] + n [\begin{matrix} 4 & - 3 \end{matrix}] = [\begin{matrix} 10 & - 11 \end{matrix}]

m

n

A = ⎡ ⎢ ⎣ \begin{matrix} - 3 & 0 & 2 1 & x & 5 - 2 & 0 & x^{2} \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 2 b - 1 \end{matrix} ⎤ ⎥ ⎦

C = [\begin{matrix} 3 & 5 & 1 \end{matrix}] .

tr

b

tr (A B C) \leq - 18

x \in R,

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