Advertisements
Advertisements
Question
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, prove that AT = A.
Solution
A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
∴ AT = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
=A.
APPEARS IN
RELATED QUESTIONS
If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`
Verify that |AB| = |A|.|B|
Simplify the following :
`{3 [(1,2,0),(0,-1,3)] - [(1,5,-2),(-3,-4,4)]} [(1),(2),(1)]`
If A = `[(2, 1), (1, 1)]` show that A2 - 3A + I = 0
A computers centre has four expert programmers . The centre needs four application programmes to be developed. The head of the computer centre , after stying carefully the programmes to be developed , estimates the computer time in minutes required by the respective experts to develop the application programmes as follows :
| Programmes | ||||
| Programmes | 1 | 2 | 3 | 4 |
| (Times in minutes) | ||||
| A | 120 | 100 | 80 | 90 |
| B | 80 | 90 | 110 | 70 |
| C | 110 | 140 | 120 | 100 |
| D | 90 | 90 | 80 | 90 |
How should the head of the computer centre assign the programmes to the programmers so that the total time required is minimum ?
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2),(0, 3)] "and C" = [(4, 3),(-1, 4),(-2, 1)]`, Show that A + B = B + A
If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]` , then find the matrix A − 2B + 6I, where I is the unit matrix of order 2.
If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix.
Find x, y, z if `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]` is a skew symmetric matrix.
For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric, or neither.
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Find matrices A and B, if 2A – B = `[(6, -6, 0),(-4, 2, 1)]` and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`.
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A + B)T = AT + BT.
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A – C)T = AT – CT.
If A = `[(-1, 2, 1),(-3, 2, -3)]` and B = `[(2, 1),(-3, 2),(-1, 3)]`, prove that (A + BT)T = AT + B.
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(1, 2, 4),(3, 2, 1),(-2, -3, 2)]`
Express each of the following matrix as the sum of a symmetric and a skew symmetric matrix `[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`.
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)T = ATBT.
Fill in the blank:
A = `[(3),(1)]` is ........................ matrix.
Fill in the blank :
If A = `[(4, x),(6, 3)]` is a singular matrix, then x is _______
State whether the following is True or False :
Every scalar matrix is unit matrix.
Solve the following :
Find k, if `[(7, 3),(5, "k")]` is a singular matrix.
Find a, b, c if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
If A = `[(1, -2),(3, -5),(-6, 0)], "B" = [(-1, -2),(4, 2),(1, 5)] and "C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.
Find matrices A and B, if `2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]`
If A = `[("i", 2"i"),(-3, 2)] and "B" = [(2"i", "i"),(2, -3)]`, where `sqrt(-1)` = i,, find A + B and A – B. Show that A + B is a singular. Is A – B a singular ? Justify your answer.
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] + [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`
There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.
July sales (in Rupees), Physics Chemistry Mathematics.
A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`
August sales(in Rupees), Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,
Find the increase in sales in Rupees from July to August 2017.
There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.
July sales (in Rupees), Physics Chemistry Mathematics.
A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`
August sales(in Rupees), Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,
If both book shops got 10 % profit in the month of August 2017, find the profit for each book seller in each subject in that month
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
Choose the correct alternative:
`[(3, 2, 1)][(2),(-2),(-1)]` = ______
State whether the following statement is True or False:
Every square matrix of order n can be expressed as sum of symmetric and skew symmetric matrix
State whether the following statement is True or False:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]` is a skew symmetric matrix
