Advertisements
Advertisements
Question
Given that A = `[(3, 0),(0, 4)]` and B = `[(a, b),(0, c)]` and that AB = A + B, find the values of a, b and c.
Solution
AB = A + B
`[(3, 0),(0, 4)][(a, b),(0, c)] = [(3, 0),(0, 4)] + [(a, b),(0, c)]`
`[(3a , 3b),(0, 4c)] = [(3 + a, b),(0 , 4 + c)]`
3a = 3 + a
2a = 3
a = `(3)/(2)`
3b = b
2b = 0
b = 0
4c = 4 + c
3c = 4
c = `(4)/(3)`.
APPEARS IN
RELATED QUESTIONS
Given matrix B = `[(1, 1),(8, 3)]`. Find the matrix X if, X = B2 – 4B. Hence, solve for a and b given `X[(a),(b)] = [(5),(50)]`.
Find the value of and 'y' if:
`2[(x,y),(9 , (y - 5))] + [(6,4),(-7,5)] = [(10,7),(22,15)]`
if `A = [(3,x),(0,1)], B = [(9,16),(0,-y)]`, Find x and y where `A^2 = B`
Evaluate:
`[(4 sin 30°, 2 cos 60°),(sin 90°, 2 cos 0°)] [(4, 5),(5, 4)]`
If A = `[(2, 1),(1, 3)]` and B = `[(3),(-11)]`, find the matrix X such that AX = B.
Evaluate the following :
`|(-2 , 3),(-1 , 4)| |(6 , 4),(3 ,- 1)|`
Evaluate x,y if
`[(3 , -2),(-1 , 4)][(2x),(1)]+2[(-4),(5)] = [(8),(4y)]`
If `[(x + 3, 4),(y - 4, x + y)] = [(5, 4),(3, 9)]`,find values of x and y
Find the values of a, b, c and d if `[(a + b, 3),(5 + c, ab)] = [(6, d),(-1, 8)]`
Find the values of a and below `[(a + 3, b^2 + 2),(0, -6)] = [(2a + 1, 3b),(0, b^2 - 5b)]`
