Advertisements
Advertisements
Question
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(4, -2),(2, 3)], "B" = [(-1, 1),(3, -2)] and "C" = [(4, 1),(2, -1)]`
Advertisements
Solution
A(B + C) = `[(4, -2),(2, 3)] {[(-1, 1),(3, -2)] + [(4, 1),(2, -1)]}`
= `[(4, -2),(2, 3)] [(-1 + 4, 1 + 1),(3 + 2, -2-1)]`
= `[(4, -2),(2, 3)][(3, 2),(5, -3)]`
= `[(12 - 10, 8 + 6),(6 + 15, 4 - 9)]`
= `[(2, 14),(21, -5)]` ...(i)
AB + AC = `[(4, -2),(2, 3)] [(-1, 1),(3, -2)] + [(4, -2),(2, 3)] [(4, 1),(2, -1)]`
= `[(-4 - 6, 4 + 4),(-2 + 9, 2 - 6)] + [(16 - 4, 4 + 2),(8 + 6, 2 - 3)]`
= `[(-10, 8),(7, -4)] + [(12, 6),(14, -1)]`
= `[(-10 + 12, 8 + 6),(7 + 14, -4 - 1)]`
= `[(2, 14),(21, -5)]` ...(ii)
From (i) and (ii), we get
A(B + C) = AB + AC
APPEARS IN
RELATED QUESTIONS
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
Verify A(BC) = (AB)C of the following case:
A = `[(1, 0, 1),(2, 3, 0),(0, 4, 5)], "B" = [(2, -2),(-1, 1),(0, 3)] and "C" = [(3, 2, -1),(2, 0, -2)]`
If A = `[(4, 3, 2),(-1, 2, 0)], "B" = [(1, 2),(-1, 0),(1, -2)]` show that matrix AB is non singular
If A = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I)
A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A2 = B.
If A = `[(8, 4),(10, 5)], "B" = [(5, -4),(10, -8)]` show that (A + B)2 = A2 + AB + B2
If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and if (A + B)2 = A2 + B2 . find values of a and b
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that `"A"^2=[(cos2alpha, sin2alpha),(-sin2alpha, cos2alpha)]`
Jay and Ram are two friends in a class. Jay wanted to buy 4 pens and 8 notebooks, Ram wanted to buy 5 pens and 12 notebooks. Both of them went to a shop. The price of a pen and a notebook which they have selected was Rs.6 and Rs.10. Using Matrix multiplication, find the amount required from each one of them
Select the correct option from the given alternatives:
If `[(5, 7),(x, 1),(2, 6)] - [(1, 2),(-3, 5),(2, y)] = [(4, 5),(4, -4),(0, 4)]` then __________
Select the correct option from the given alternatives:
If A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______
Select the correct option from the given alternatives:
If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______
Answer the following question:
If f(α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(– α)
Answer the following question:
If f (α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(–α) + f(α)
Answer the following question:
If Aα = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that Aα . Aβ = Aα+β
Answer the following question:
If A = `[(2, -2, -4),(-1, 3, 4),(1, -2, -3)]` show that A2 = A
Answer the following question:
If A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A2 = I
Answer the following question:
If A = `[(2, -1),(-1, 2)]`, show that A2 – 4A + 3I = 0
Answer the following question:
if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A2 – B2 , find x and y
Answer the following question:
If A = `[(2, -1),(3, -2)]`, find A3
Answer the following question:
Find x, y if, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`
Answer the following question:
Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)]` and I is the unit matrix of order 3, then A2 + 2A4 + 4A6 is equal to ______.
Which description correctly states matrix multiplication?
If \[A\] is \[m \times n\] and \[B\] is \[n \times p\], what is the order of \[AB\]?
Which statement describes the general relationship between \[AB\] and \[BA\]?
Which property is an associative property of matrix multiplication?
Which equation expresses that the identity matrix acts as a multiplicative identity?
Which equation expresses that the zero matrix absorbs multiplication?
