Advertisements
Advertisements
प्रश्न
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.
उत्तर
A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`
∴ AT = `[(2, 3, 4),(-1, -2, 1)] "and B"^"T" = [(0, 2),(3, -1),(-4, 1)]`
AB = `[(2, -1),(3, -2),(4, 1)][(0, 3, -4),(2, -1, 1)]`
= `[(0 - 2, 6 + 1, -8 - 1),(0 - 4, 9 + 2, -12 - 2),(0 + 2, 12 - 1, -16 + 1)]`
= `[(-2, 7, -9),(-4, 11, -14),(2, 11, -15)]`
∴ (AB)T = `[(-2, -4, 2),(7, 11, 11),(-9, -14, -15)]` ...(i)
BTAT = `[(0, 2),(3, -1),(-4, 1)][(2, 3, 4),(-1, -2, 1)]`
= `[(0 - 2, 0 - 4, 0 + 2),(6 + 1, 9 + 2, 12 - 1),(-8 - 1, -12 - 2, -16 + 1)]`
= `[(-2, -4, 2),(7, 11, 11),(-9, -14, -15)]` ...(ii)
From (i) and (ii), we get
(AB)T = BTAT.
APPEARS IN
संबंधित प्रश्न
Find the values of x and y if
`2 [(x,5),(7,y-3)] [(3,-4),(1,2)] = [(7,6),(15,14)]`
Solve the following equations by reduction method:
x + y + z = 6,
3x - y + 3z = 10
5x + y - 4z = 3
Solve the following equations by reduction method:
x+ y+z = 6,
3x-y+3z = 10
5x+ y-4z = 3
Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`
If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.
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 = `[(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.
If A = `[(5, 1, -4),(3, 2, 0)]`, find (AT)T.
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, find (AT)T.
Find a, b, c, if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
Find matrices A and B, if 2A – B = `[(6, -6, 0),(-4, 2, 1)]` and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`.
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`.
If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and (A + B)2 = A2 + B2, find the values of a and b.
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
If A = `[(5, -3),(4, -3),(-2, 1)]`, prove that (AT)T = A.
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, prove that AT = A.
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(5, 2, -4),(3, -7, 2),(4, -5, -3)]`
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)T = ATBT.
Choose the correct alternative.
If A = `[(α, 4),(4, α)]` and |A3| = 729, then α = ______.
Fill in the blank :
Matrix B = `[(0, 3, 1),(-3, 0, -4),("p", 4, 0)]` is skew symmetric, then the value of p is _______
State whether the following is True or False :
If A and B are square matrices of same order, then (A + B)2 = A2 + 2AB + B2.
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
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)]`
If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.
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.
Evaluate : `[2 -1 3][(4),(3),(1)]`
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
Answer the following question:
Find matrices A and B, where 3A – B = `[(-1, 2, 1),(1, 0, 5)]` and A + 5B = `[(0, 0, 1),(-1, 0, 0)]`
Answer the following question:
If A = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, B = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, show that BA = 6I
Choose the correct alternative:
For any square matrix B, matrix B + BT is ______
Choose the correct alternative:
If A and B are two square matrices of order 3, then (AB)T = ______
If `A = [(-3,2),(2,4)], B = [(1,a),(b,0)] "and" (A + B)(A-B) = A^2 - B^2, "Find" a "and" b`
