Advertisements
Advertisements
प्रश्न
For the non singular matrix A, (A′)–1 = (A–1)′.
पर्याय
True
False
उत्तर
This statement is True.
APPEARS IN
संबंधित प्रश्न
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.
Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Choose the correct alternative.
The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(6, 0),(0, 6)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A
Answer the following question:
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
State whether the following statement is True or False:
If A is non singular, then |A| = 0
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
For any square matrix A, AAT is a ____________.
A matrix is said to be a column matrix if it has
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
If D = `[(0, aα^2, aβ^2),(bα + c, 0, aγ^2),(bβ + c, (bγ + c), 0)]` is a skew-symmetric matrix (where α, β, γ are distinct) and the value of `|((a + 1)^2, (1 - a), (2 - c)),((3 + c), (b + 2)^2, (b + 1)^2),((3 - b)^2, b^2, (c + 3))|` is λ then the value of |10λ| is ______.
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.
If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.
A matrix which is both symmetric and skew symmetric matrix is a ______.
