Advertisements
Advertisements
प्रश्न
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
Advertisements
उत्तर
We have, AB = 2I
`|"AB"| = |2"I"|`
⇒ `|"A"| |"B"| = 8`
⇒ `2 |"B"| = 8 ...("Given" |"A"| = 2)`
⇒ `|"B"| = 4`
APPEARS IN
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Find the value of x, y and z from the following equation:
`[(4, 3),(x, 5)] = [(y, z),(1, 5)]`
Find the value of x, y and z from the following equation:
`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
Given two matrices A and B
`A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`
find AB and use this result to solve the following system of equations:
x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.
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:
`[(5),(4),(-3)]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Find k if the following matrix is singular:
`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
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:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
Choose the correct alternative:
If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______
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
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
If a matrix A is both symmetric and skew-symmetric, then ____________.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
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
Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
If A is a square matrix of order 3, then |2A| is equal to ______.
Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100
Reason: AB = BA implies AB = BA for all positive integers n.
