If the sum of three matrices is given as - A - B - C - begin bmatrix 0 - 5 - 4 58882116-0-0bmatrix -then what is A - B - C -A- - 58882116-0-0bmatrix-B- -beginbmatrix 0 - 5 - 6 5 - 880 14-2-0bmatrix -C- - -beginbmatrix 0 - 0 - 0 080 - 011D- Cannot determine

The correct option is A [ 0 amp;5 amp;4; 5 amp;8 amp;2; 6 amp;0 amp;0 ]We know that matrix addition follows associative property. ∴ A+(B+C) = (A+B) ...

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Standard X

Mathematics

Properties of Matrix Addition

If the sum of...

Question

If the sum of three matrices is given as
$A + (B + C) = ⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 4 5 & 8 & 2 6 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦,$
then what is $(A + B) + C ?$

⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 4 5 & 8 & 2 6 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 6 5 & 8 & 0 4 & 2 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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Cannot determine

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Solution

The correct option is A $⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 4 5 & 8 & 2 6 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$
We know that matrix addition follows associative property.
$∴ A + (B + C) = (A + B) + C H e n c e, (A + B) + C = ⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 4 5 & 8 & 2 6 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q. Given, for a matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 5 & 3 & 5 2 & 3 & 8 0 & 3 & 0 \end{matrix} ⎤ ⎥ ⎦,

what will be its additive identity?

Q. If

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

then

A^{16}

Q. Given the matrices

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & 1 3 & - 1 & 0 0 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 9 & 7 & - 1 3 & 5 & 4 2 & 1 & 6 \end{matrix} ⎤ ⎥ ⎦

and

C = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 4 & 3 1 & - 1 & 0 9 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦

Verify that

(A + B) + C = A + (B + C)

Q. If a, b, c, d denote the determinants of matrices A, B, C, D where
A=

⎡ ⎢ ⎣ \begin{matrix} 0 & x - y & x - z y - x & 0 & y - z z - x & z - y & 0 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 3 & 4 4 & 9 & 16 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 2 0 & 5 & 0 7 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & 8 1 & 3 & 27 \end{matrix} ⎤ ⎥ ⎦

Then the ascending order of a, b, c, d

Q. Let

A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & - 3 3 & 4 & 5 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦, B = [\begin{matrix} 1 & - 2 - 1 & 2 \end{matrix}]

and

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

. If

a, b

and

c

respectively denote the ranks of

A, B

and

C

then the correct order of these numbers is

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If the sum of three matrices is given as A+(B+C)=⎡⎢⎣054582600⎤⎥⎦, then what is (A+B)+C ?

The correct option is A ⎡⎢⎣054582600⎤⎥⎦We know that matrix addition follows associative property. ∴A+(B+C)=(A+B)+CHence, (A+B)+C=⎡⎢⎣054582600⎤⎥⎦

If the sum of three matrices is given as
$A + (B + C) = ⎡ ⎢ ⎣ \begin{matrix} 0 & 5 & 4 5 & 8 & 2 6 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦,$
then what is $(A + B) + C ?$