Advertisements
Advertisements
प्रश्न
If A is a square matrix of order 3, then |2A| is equal to ______.
विकल्प
2|A|
4|A|
8|A|
6|A|
Advertisements
उत्तर
If A is a square matrix of order 3, then |2A| is equal to 8|A|.
Explanation:
Order of square matrix A.
n = 3
∵ |kA| = kn|A|,
k = constant
`\implies` |2A| = 23|A|
= 8|A|
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.
If A = `[(0, -tan α/2), (tan α/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I - A)[(cos α, -sin α),(sin α, cos α)]`
if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O
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
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
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:
`[(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:
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Identify the following matrix is singular or non-singular?
`[(7, 5),(-4, 7)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
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 _______
State whether the following statement is True or False:
If A is non singular, then |A| = 0
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
If two matrices A and B are of the same order, then 2A + B = B + 2A.
For the non singular matrix A, (A′)–1 = (A–1)′.
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If A is a square matrix, then A – A’ is a ____________.
If a matrix A is both symmetric and skew-symmetric, then ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
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 ______.
If A = `[(0, -tan θ/2),(tan θ/2, 0)]` and (I2 + A) (I2 – A)–1 = `[(a, -b),(b, a)]` then 13(a2 + b2) 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.
A matrix which is both symmetric and skew symmetric matrix is a ______.
Matrices are classified into different types based on which two features?
What is the order of \[A=\begin{bmatrix}0\\ \sqrt{3}\\ -1\\ \dfrac{1}{2}\end{bmatrix}\]?
What is the order of a row matrix with \[n\] columns?
If \[m=n\], what type and order does the matrix have?
Which condition holds for a diagonal matrix when \[i\ne j\]?
Which statement correctly describes the relationship between scalar matrices and diagonal matrices?
How is an identity matrix denoted when its order is \[n\]?
Which matrix is an identity matrix?
What role does the zero matrix play in matrix algebra?
Which matrix is a zero matrix?
