1
Question
If A=⎡⎢⎣204628246⎤⎥⎦,B=⎡⎢⎣84−20−20226⎤⎥⎦ and C=⎡⎢⎣8200−2−6−84−10⎤⎥⎦Compute (3A+2B)−3C
If A=⎡⎢⎣204628246⎤⎥⎦,B=⎡⎢⎣84−20−20226⎤⎥⎦ and C=⎡⎢⎣8200−2−6−84−10⎤⎥⎦
Compute (3A+2B)−3C
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Solution
3A=3⎡⎢⎣204628246⎤⎥⎦=⎡⎢⎣60121862461218⎤⎥⎦2B=2⎡⎢⎣84−20−20226⎤⎥⎦=⎡⎢⎣168−40−404412⎤⎥⎦3A+2B=⎡⎢⎣60121862461218⎤⎥⎦+⎡⎢⎣168−40−404412⎤⎥⎦=⎡⎢⎣6+160+812−418+06−424+06+412+418+12⎤⎥⎦=⎡⎢⎣228818224101630⎤⎥⎦∴3A+2B=⎡⎢⎣228818224101630⎤⎥⎦3C=3⎡⎢⎣8200−2−6−84−10⎤⎥⎦=⎡⎢⎣24600−6−18−2412−30⎤⎥⎦(3A+2B)−3C=⎡⎢⎣228818224101630⎤⎥⎦−⎡⎢⎣24600−6−18−2412−30⎤⎥⎦=⎡⎢⎣22−248−68−018−02−624+1810+2416−1230+30⎤⎥⎦=⎡⎢⎣−22818−44234460⎤⎥⎦
3A=3⎡⎢⎣204628246⎤⎥⎦
=⎡⎢⎣60121862461218⎤⎥⎦
2B=2⎡⎢⎣84−20−20226⎤⎥⎦
=⎡⎢⎣168−40−404412⎤⎥⎦
3A+2B=⎡⎢⎣60121862461218⎤⎥⎦+⎡⎢⎣168−40−404412⎤⎥⎦
=⎡⎢⎣6+160+812−418+06−424+06+412+418+12⎤⎥⎦
=⎡⎢⎣228818224101630⎤⎥⎦
∴3A+2B=⎡⎢⎣228818224101630⎤⎥⎦
3C=3⎡⎢⎣8200−2−6−84−10⎤⎥⎦
=⎡⎢⎣24600−6−18−2412−30⎤⎥⎦
(3A+2B)−3C=⎡⎢⎣228818224101630⎤⎥⎦−⎡⎢⎣24600−6−18−2412−30⎤⎥⎦
=⎡⎢⎣22−248−68−018−02−624+1810+2416−1230+30⎤⎥⎦
=⎡⎢⎣−22818−44234460⎤⎥⎦
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