Advertisements
Advertisements
प्रश्न
For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
उत्तर
Let A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = `[(0, -1 - 2"i", 2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)]`
∴ AT = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = – A i.e. A = – AT
∴ A is a skew-symmetric matrix.
APPEARS IN
संबंधित प्रश्न
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)]`
Solve the following equations by reduclion method
x+3y+3z= 16 , x+4y+4z=21 , x+3y+4z = 19
Solve the following equations by reduction method :
x + 2y + z = 8
2x+ 3y - z = 11
3x - y - 2z = 5
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 ?
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.
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
Construct the matrix A = [aij]3×3 where aij = i − j. State whether A is symmetric or skew-symmetric.
Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]` and X – 3Y = `[(0, -1),(0, -1)]`.
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
If [aij]3×3, where aij = 2(i – j), find A and AT. State whether A and AT both are symmetric or skew-symmetric matrices?
If A = `[(5, -3),(4, -3),(-2, 1)]`, prove that (AT)T = A.
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 = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find 5AT – 5BT.
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)]`
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.
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.
State whether the following is True or False :
Every scalar matrix is unit matrix.
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.
Find a, b, c if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
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, -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.
Simplify, `costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`
If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.
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 = ______
In a Skew symmetric matrix, all diagonal elements are ______
If `A = [(-3,2),(2,4)], B = [(1,a),(b,0)] "and" (A + B)(A-B) = A^2 - B^2, "Find" a "and" b`
Find the x, y, z, if `{3[(2,0),(0,2),(2,2)]-4[(1,1),(-1,2),(3,1)]}[(1),(2)]=[(x-3),(y-1),( 2z)]`
