Let A=⎡⎢⎣100210321⎤⎥⎦
If u1 and u2 are column matrices such that Au1=⎡⎢⎣100⎤⎥⎦ and Au2=⎡⎢⎣010⎤⎥⎦, then u1+u2 is equal to
A
⎡⎢⎣−110⎤⎥⎦
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B
⎡⎢⎣−11−1⎤⎥⎦
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C
⎡⎢⎣−1−10⎤⎥⎦
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D
⎡⎢⎣1−1−1⎤⎥⎦
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Solution
The correct option is D
⎡⎢⎣1−1−1⎤⎥⎦
Let u1=⎡⎢⎣abc⎤⎥⎦u2=⎡⎢⎣def⎤⎥⎦ Au1=⎡⎢⎣a2a+b3a+2b+c⎤⎥⎦=⎡⎢⎣100⎤⎥⎦ a=1,b=−2,c=1 u1⎡⎢⎣1−21⎤⎥⎦ Au2=⎡⎢⎣d2d+e3d+2e+f⎤⎥⎦=⎡⎢⎣010⎤⎥⎦ u2=⎡⎢⎣01−2⎤⎥⎦ u1+u2=⎡⎢⎣1−1−1⎤⎥⎦