EXAMPLE 2 Let A = diag [3, -5, 7] a...
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EXAMPLE 2 Let A = diag [3, -5, 7] and B = diag (-1, 2, 4]. Find (i) (A + B) (ii) (A - B) (iii) -5A (iv) (2A + 3B).

11th - 12th Class
Maths
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solution We have [ A=left[begin{array}{rrr} 3 & 0 & 0 0 & -5 & 0 0 & 0 & 7 end{array}right] text { and } B=left[begin{array}{rrr} -1 & 0 & 0 0 & 2 & 0 0 & 0 & 4 end{array}right] ] (i) ( A+B=left[begin{array}{rrr}3 & 0 & 0 0 & -5 & 0 0 & 0 & 7end{array}right]+left[begin{array}{rrr}-1 & 0 & 0 0 & 2 & 0 0 & 0 & 4end{array}right]=left[begin{array}{rrr}2 & 0 & 0 0 & -3 & 0 0 & 0 & 11end{array}right] ) (ii) ( (A-B)=A+(-B) ) [ =left[begin{array}{rrr} 3 & 0 & 0 0 & -5 & 0 0 & 0 & 7 end{array}right]+left[begin{array}{rrr} 1 & 0 & 0 0 & -2 & 0 0 & 0 & -4 end{array}right]=left[begin{array}{rrr} 4 & 0 & 0 0 & -7 & 0 0 & 0 & 3 end{array}right] ] ( left(begin{array}{cccc}text { (iii) }-5 A=(-5) cdot A=(-5) & cdotleft[begin{array}{lrr}3 & 0 & 0 0 & -5 & 0 0 & 0 & 7end{array}right] & =left[begin{array}{rrr}-15 & 0 & 0 0 & 25 & 0 0 & 0 & -35end{array}right]end{array}right. ) (iv) ( 2 A+3 B=left[begin{array}{rrr}6 & 0 & 0 0 & -10 & 0 0 & 0 & 14end{array}right]+left[begin{array}{rrr}-3 & 0 & 0 0 & 6 & 0 0 & 0 & 12end{array}right]=left[begin{array}{rrr}3 & 0 & 0 0 & -4 & 0 0 & 0 & 26end{array}right] )
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