Advertisements
Advertisements
प्रश्न
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
उत्तर
`A + A^T=[(2 4),(3 5)] + [(2 3),(4 5)] = [(4 7),(7 10)]`
∴ `(A + A^T)^T = [(4 7),(7 10)]=(A + A^T)`
∴ A + AT is symmetric matrix.
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:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
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| .
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
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)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
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 = `[(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.
AB = AC ⇒ B = C for any three matrices of same order.
Show by an example that for A ≠ O, B ≠ O, AB = O
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 is a square matrix, then A – A’ is a ____________.
The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.
The matrix A `=[(0,1),(1,0)]` is a ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
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 ______.
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 ______.
The minimum number of zeros in an upper triangular matrix will be ______.
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
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 ______.
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
