Advertisements
Advertisements
Question
Answer the following question:
If A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A2 = I
Advertisements
Solution
A2 = A·A
= `[(4, -1, -4),(3, 0, -4),(3, -1, -3)] [(4, -1, -4),(3, 0, -4),(3, -1, -3)]`
= `[(16 - 3 - 12, -4 + 0 + 4, -16 + 4 + 12),(12 + 0 - 12, -3 + 0 + 4, -12 + 0 + 12),(12 - 3 - 9, -3 - 0 + 3, -12 + 4 + 9)]`
= `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
= I
APPEARS IN
RELATED QUESTIONS
Show that AB = BA where,
A = `[(costheta, - sintheta),(sintheta, costheta)], "B" = [(cosphi, -sinphi),(sinphi, cosphi)]`
If A = `[(4, 8),(-2, -4)]`, prove that A2 = 0
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)]`
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 = `[(3, 4),(-4, 3)] and "B" = [(2, 1),(-1, 2)]`, show that (A + B)(A – B) = A2 – B2
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 and y, if `{4[(2, -1, 3),(1, 0, 2)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`
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)]`
If A = `[(1, 2),(3, 5)]` B = `[(0, 4),(2, -1)]`, show that AB ≠ BA, but |AB| = IAl·IBI
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 = `[(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, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`
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 total sale in rupees for two months of each farmer for each crop
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 statement describes the general relationship between \[AB\] and \[BA\]?
Which equation shows that matrix multiplication is distributive over addition?
