Given A- 3 1- -2 1 - and B- 4 -3- 2 -1 -Find sum of all elements in the matrix A-B-2I-4 marks-

A+B=[ 3 amp; 1; nbsp; 2 amp; 1 ]+[ nbsp;4 amp; 3; nbsp; 2 amp; 1 nbsp; ]=[ 7 amp; 2; nbsp; 0 amp;0 nbsp; ] [1 mark] nbsp ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

Given A=[ 3 1...

Question

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

Find sum of all elements in the matrix A+B-2I.

[4 marks]

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Solution

$A + B = [\begin{matrix} 3 & 1 - 2 & 1 \end{matrix}] + [\begin{matrix} 4 & - 3 2 & - 1 \end{matrix}] = [\begin{matrix} 7 & - 2 0 & 0 \end{matrix}]$

[1 mark]

$2 I = [\begin{matrix} 2 & 0 0 & 2 \end{matrix}]$

[1 mark]

$A + B - 2 I = [\begin{matrix} 7 & - 2 0 & 0 \end{matrix}] - [\begin{matrix} 2 & 0 0 & 2 \end{matrix}] = [\begin{matrix} 5 & - 2 0 & - 2 \end{matrix}]$

[1 mark]

Sum of all elements in A+B-2I
= 5 + 0 + (-2) + (-2) = 5 - 4 = 1

[1 mark]

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Given A=[31−21] and B=[4−32−1] Find sum of all elements in the matrix A+B-2I. [4 marks]

A+B=[31−21]+[4−32−1]=[7−200] [1 mark] 2I=[2002] [1 mark] A+B−2I=[7−200]−[2002]=[5−20−2] [1 mark] Sum of all elements in A+B-2I = 5 + 0 + (-2) + (-2) = 5 - 4 = 1 [1 mark]

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

Find sum of all elements in the matrix A+B-2I.

[4 marks]