Advertisements
Advertisements
प्रश्न
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
Advertisements
उत्तर
A2 = A · A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)] [(1, 2, 2),(2, 1, 2),(2, 2, 1)]`
= `[(1 + 4 + 4, 2 + 2 + 4, 2 + 4 + 2),(2 + 2 + 4, 4 + 1 + 4, 4 + 2 + 2),(2 + 4 + 2, 4 + 2 + 2, 4 + 4 + 1)]`
= `[(9, 8, 8),(8, 9, 8),(8, 8, 9)]`
∴ A2 – 4A = `[(9, 8, 8),(8, 9, 8),(8, 8, 9)] - 4[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`
= `[(9, 8, 8),(8, 9, 8),(8, 8, 9)] -[(4, 8, 8),(8, 4, 8),(8, 8, 4)]`
= `[(5, 0, 0),(0, 5, 0),(0, 0, 5)]`
which is a scalar matrix.
APPEARS IN
संबंधित प्रश्न
`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.
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 the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
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, 4, 7),(-4, 0, -3),(-7, 3, 0)]`
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]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Identify the following matrix is singular or non-singular?
`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
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
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
If two matrices A and B are of the same order, then 2A + B = B + 2A.
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`
If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
A matrix is said to be a column matrix if it has
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
If the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.
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 ______.
The minimum number of zeros in an upper triangular matrix will be ______.
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
