If A = [5−53−3] and B=[−55−33]\begin{bmatrix}[r] 5 & -5 \ 3 & -3 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -5 & 5 \ -3 & 3 \end{bmatrix}[53−5−3] and B=[−5−353]; the value of matrix (A - B) is :
[0000]\begin{bmatrix}[r] 0 & 0 \ 0 & 0 \end{bmatrix}[0000]
[10−106−6]\begin{bmatrix}[r] 10 & -10 \ 6 & -6 \end{bmatrix}[106−10−6]
[10−10−66]\begin{bmatrix}[r] 10 & -10 \ -6 & 6 \end{bmatrix}[10−6−106]
[−1010−66]\begin{bmatrix}[r] -10 & 10 \ -6 & 6 \end{bmatrix}[−10−6106]
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Given,
A = [5−53−3] and B=[−55−33]\begin{bmatrix}[r] 5 & -5 \ 3 & -3 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -5 & 5 \ -3 & 3 \end{bmatrix}[53−5−3] and B=[−5−353]
A−B=[5−53−3]−[−55−33]=[5−(−5)−5−53−(−3)−3−3]=[10−106−6]A -B = \begin{bmatrix}[r] 5 & -5 \ 3 & -3 \end{bmatrix} - \begin{bmatrix}[r] -5 & 5 \ -3 & 3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 5 - (-5) & -5 - 5 \ 3 - (-3) & -3 - 3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 10 & -10 \ 6 & -6 \end{bmatrix}A−B=[53−5−3]−[−5−353]=[5−(−5)3−(−3)−5−5−3−3]=[106−10−6]
Hence, Option 2 is the correct option.
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If [x+27y+3a−2]=[4b−343]\begin{bmatrix}[r] x + 2 & 7 \ y + 3 & a - 2 \end{bmatrix} = \begin{bmatrix}[r] 4 & b - 3 \ 4 & 3 \end{bmatrix}[x+2y+37a−2]=[44b−33], the value of x, y, a and b are :
x = 2, y = 1, a = 5 and b = 10
x = -2, y = 1, a = 5 and b = 10
x = 2, y = -1, a = 5 and b = 10
x = 2, y = 1, a = -5 and b = 10
If A = [5540],B=[3214] and C=[−2321]\begin{bmatrix}[r] 5 & 5 \ 4 & 0 \end{bmatrix}, B = \begin{bmatrix}[r] 3 & 2 \ 1 & 4 \end{bmatrix} \text{ and } C = \begin{bmatrix}[r] -2 & 3 \ 2 & 1 \end{bmatrix}[5450],B=[3124] and C=[−2231] then matrix (A + B - C) is :
[104−33]\begin{bmatrix}[r] 10 & 4 \ -3 & 3 \end{bmatrix}[10−343]
[−1043−3]\begin{bmatrix}[r] -10 & 4 \ 3 & -3 \end{bmatrix}[−1034−3]
[10433]\begin{bmatrix}[r] 10 & 4 \ 3 & 3 \end{bmatrix}[10343]
[10−433]\begin{bmatrix}[r] 10 & -4 \ 3 & 3 \end{bmatrix}[103−43]
If A = [75−33] and B=[−2510]\begin{bmatrix}[r] 7 & 5 \ -3 & 3 \end{bmatrix} \text{ and B} = \begin{bmatrix}[r] -2 & 5 \ 1 & 0 \end{bmatrix}[7−353] and B=[−2150], then the matrix P (such that A + P = B) is :
[409−3]\begin{bmatrix}[r] 4 & 0 \ 9 & -3 \end{bmatrix}[490−3]
[904−2]\begin{bmatrix}[r] 9 & 0 \ 4 & -2 \end{bmatrix}[940−2]
[−9043]\begin{bmatrix}[r] -9 & 0 \ 4 & 3 \end{bmatrix}[−9403]
[−904−3]\begin{bmatrix}[r] -9 & 0 \ 4 & -3 \end{bmatrix}[−940−3]
The additive inverse of matrix A + B, where
A = [427−2] and B=[−213−4]\begin{bmatrix}[r] 4 & 2 \ 7 & -2 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -2 & 1 \ 3 & -4 \end{bmatrix}[472−2] and B=[−231−4] is :
[−2−3−106]\begin{bmatrix}[r] -2 & -3 \ -10 & 6 \end{bmatrix}[−2−10−36]
[23−10−6]\begin{bmatrix}[r] 2 & 3 \ -10 & -6 \end{bmatrix}[2−103−6]
[−2−3−10−6]\begin{bmatrix}[r] -2 & -3 \ -10 & -6 \end{bmatrix}[−2−10−3−6]
[−2310−6]\begin{bmatrix}[r] -2 & 3 \ 10 & -6 \end{bmatrix}[−2103−6]
