Advertisements
Advertisements
Question
If A = `[(2, a),(-3, 5)] and "B" = [(-2, 3),(7, b)], "C" = [(c, 9),(-1, -11)]` and 5A + 2B = C, find the values of a,b,c
Solution
A = `[(2, a),(-3, 5)] and "B" = [(-2, 3),(7, b)], "C" = [(c, 9),(-1, -11)]` and 5A + 2B = C
⇒ `5[(2, a),(-3, 5)] + 2[(-2, 3),(7, b)] = [(c, 9),(-1, -11)]`
⇒ `[(10, 5a),(-15, 25)] + [(-4, 6),(14, 2b)] = [(c, 9),(-1, -11)]`
⇒ `[(10 - 4, 5a + 6),(15 + 14, 25 + 2b)] = [(c, 9),(-1, -11)]`
⇒ `[(6, 5a + 6),(-1, 25 + 2b)] = [(c, 9),(-1, -11)]`
Comparing each term
5a + 6 = 9
⇒ 5a = 9 – 6 = 3
⇒ a = `(3)/(5)`
⇒ 25 + 2b = –11
⇒ 2b = –11 – 25 = –36
⇒ b = `-(36)/(2)` = –18
c = 6
Hence a = `(3)/(5)`, b = –18 and c = 6.
APPEARS IN
RELATED QUESTIONS
Given `A = [(-1, 0),(2, -4)]` and `B = [(3, -3),(-2, 0)]`; find the matrix X in the following:
X – B = A
If A = `[(0, 2),(5, -2)]`, B =` [(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find AI
If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find B2A
Given `A = [(4, 1), (2,3)] and B = [(1, 0),(-2, 1)]` Find `A^2 - AB + 2B`
If A = `[(1, 2),(3, 4)]`, B = `[(6, 1), (1, 1)]` and C = `[(-2, -3),(0, 1)]`, find the following and state if they are equal CA + B
If A = `[(1, 2),(3, 4)]`, B = `[(6, 1),(1, 1)]` and C = `[(-2, -3),(0, 1)]`, find the following and state if they are equal A + CB
If P =`|(1 , 2),(3 , 4)|` , Q = `|(5 , 1),(7 , 4)|` and R = `|(2 , 1),(4 , 2)|` find the value of (R + Q)P
Given
`"A" = [(2 , -6),(2, 0)] "B" = [(-3, 2),(4, 0)], "C" = [(4, 0),(0, 2)]`
Find the martix X such that A + 2X = 2B + C.
Solve the matrix equation `[(2, 1),(5, 0)] -3"X" = [(-7, 4),(2, 6)]`
Find X and Y If X + Y = `[(7, 0),(2, 5)]` and X – Y = `[(3, 0),(0, 3)]`
