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Exercise: Matrix Addition and Scalar ... · Q16

Q.For the matrices AA and BB of Q1, find the matrix XX such that A+X=BA+X=B.

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From A+X=BA+X=B, adding −A-A to both sides gives X=B−AX=B-A. Computing entrywise: (1,1)(1,1): 1−2=−11-2=-1; (1,2)(1,2): 4−(−1)=54-(-1)=5; (2,1)(2,1): −2−0=−2-2-0=-2; (2,2)(2,2): 5−3=25-3=2. So X=[−15−22]X=\begin{bmatrix}-1&5\\-2&2\end{bmatrix}. Checking: $A+X=\begin{bmatrix}2-1&-1+5\0-2&3+2\end{bmatrix}=\beg …

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