Advertisements
Advertisements
Question
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Solution 1
Given A (adj A = `[(8,0),(0,8)]`
we know that A(adj A) = |A| - I
|A|.I = `8[(1,0),(0,1)]`
`=> |A| = 8`
Solution 2
It is given that
A(adj A) = `[(8,0),(0,8)]`
⇒ A(adj A) = `8[(1,0),(0,1)]`
⇒ A(adj A) = 8I2 .....(1)
We know that for any square matrix A of order 2, we have
A(adj A) = |A|I2 .....(2)
From (1) and (2), we have
|A|=8
RELATED QUESTIONS
If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.
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.
Find the value of x, y, and z from the following equation:
`[(4,3),(x,5)] = [(y,z),(1,5)]`
Let A = `[(0,1),(0,0)]`show that (aI+bA)n = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N
If A is a square matrix such that A2 = A, then (I + A)3 – 7 A is equal to ______.
if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'
If ЁЭТЩ = r cos θ and y= r sin θ prove that JJ-1=1.
If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
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:
`[9 sqrt(2) -3]`
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:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`
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)]`
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:
`[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`
Find k if the following matrix is singular:
`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
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
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
If two matrices A and B are of the same order, then 2A + B = B + 2A.
AB = AC ⇒ B = C for any three matrices of same order.
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
If a matrix A is both symmetric and skew-symmetric, then ____________.
If `[(1,2),(3,4)],` then A2 - 5A 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 ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
