Question
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] )

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).
Solution
