Advertisements
Advertisements
Question
Answer the following question:
If A = `[(0, 1),(1, 0)]` and B = `[(0, -1),(1, 0)]` show that (A + B)(A – B) ≠ A2 – B2
Advertisements
Solution
A + B = `[(0, 1),(1, 0)] + [(0, -1),(1, 0)]`
= `[(0, 0),(2, 0)]`
A – B = `[(0, 1),(1, 0)] - [(0, -1),(1, 0)]`
= `[(0, 2),(0, 0)]`
∴ (A + B)(A – B) = `[(0, 0),(2, 0)] [(0, 2),(0, 0)]`
= `[(0 + 0, 0 + 0),(0 + 0, 4 + 0)]`
= `[(0, 0),(0, 4)]` ...(1)
Also, A2 = A·A = `[(0, 1),(1, 0)] [(0, 1),(1, 0)]`
= `[(0 + 1, 0 + 0),(0 + 0, 1 + 0)]`
= `[(1, 0),(0, 1)]`
B2 = B·B = `[(0, -1),(1, 0)] [(0, -1),(1, 0)]`
= `[(0 - 1, 0 - 0),(0 + 0, -1 + 0)]`
= `[(-1, 0),(0, -1)]`
∴ A2 – B2 = `[(1, 0),(0, 1)] - [(-1, 0),(0, -1)]`
= `[(2, 0),(0, 2)]`
From (1) and (2),
(A+ B)(A – B) ≠ A2 – B2.
APPEARS IN
RELATED QUESTIONS
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
If A = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)], "B" = [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`. State whether AB = BA? Justify your answer.
If A = `[(4, 8),(-2, -4)]`, prove that A2 = 0
Verify A(BC) = (AB)C of the following case:
A = `[(2, 4, 3),(-1, 3, 2)], "B" = [(2, -2),(3, 3),(-1, 1)], "C" = [(3, 1),(1, 3)]`
Verify that A(B + C) = AB + AC of the following matrix:
A = `[(1, -1, 3),(2, 3, 2)], "B" = [(1, 0),(-2, 3),(4, 3)], "C" = [(1, 2),(-2, 0),(4, -3)]`
If A = `[(1, -2),(5, 6)], "B" = [(3, -1),(3, 7)]`, Find AB - 2I, where I is unit matrix of order 2.
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
Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`
Find k, if A= `[(3, -2),(4, -2)]` and if A2 = kA – 2I
Find x, if `[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0
Find x, y, z if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)]` = `[("x" - 3),("y" - 1),(2"z")]`
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 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 A = `[(-2, 1),(0, 3)]` and f(x) = 2x2 – 3x, then f(A) = ………
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 A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A2 = I
Answer the following question:
If A = `[(3, -5),(-4, 2)]`, show that A2 – 5A – 14I = 0
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, `[(0, -1, 4)]{2[(4, 5),(3, 6),(2, -1)] + 3[(4, 3),(1, 4),(0, -1)]} = [(x, y)]`
Answer the following question:
Find x, y, z if `{[(1, 3, 2),(2, 0, 1),(3, 1, 2)] + 2[(3, 0, 2),(1, 4, 5),(2, 1, 0)]} [(1),(2),(3)] = [(x),(y),(z)]`
Answer the following question:
Two farmers Shantaram and Kantaram cultivate three crops rice,wheat and groundnut. The sale (In Rupees) of these crops by both the farmers for the month of April and may 2008 is given below,
| April sale (In Rs.) | |||
| Rice | Wheat | Groundnut | |
| Shantaram | 15000 | 13000 | 12000 |
| Kantaram | 18000 | 15000 | 8000 |
| May sale (In Rs.) | |||
| Rice | Wheat | Groundnut | |
| Shantaram | 18000 | 15000 | 12000 |
| Kantaram | 21000 | 16500 | 16000 |
Find the increase in sales from April to May for every crop of each farmer.
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?
For which condition does the product \[AB\] exist?
If \[A\] is \[m \times n\] and \[B\] is \[n \times p\], what is the order of \[AB\]?
Which property is an associative property of matrix multiplication?
Which equation expresses that the zero matrix absorbs multiplication?
