Advertisements
Advertisements
प्रश्न
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
Advertisements
उत्तर
Let A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = `[(0, -1 - 2"i", 2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)]`
∴ AT = `-[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = – A, i.e., A = –AT
∴ A is a skew-symmetric matrix.
APPEARS IN
संबंधित प्रश्न
Find the value of x, y, and z from the following equation:
`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`
Find the value of a, b, c and d from the equation:
`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`
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 = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
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)]`
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)]`
Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.
Select the correct option from the given alternatives:
If A and B are square matrices of equal order, then which one is correct among the following?
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
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 `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
AB = AC ⇒ B = C for any three matrices of same order.
Show by an example that for A ≠ O, B ≠ O, AB = O
A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.
The matrix A `=[(0,1),(1,0)]` is a ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
If a matrix A is both symmetric and skew symmetric then matrix A is ____________.
Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements:
(P) If A1I2, then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,
where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then ______.
What is the order of \[A=\begin{bmatrix}0\\ \sqrt{3}\\ -1\\ \dfrac{1}{2}\end{bmatrix}\]?
A matrix with only one row is called a:
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 elements can be non-zero in a diagonal matrix?
An identity matrix (unit matrix) is a square matrix with:
How is an identity matrix denoted when its order is \[n\]?
Which matrix is an identity matrix?
