If A is a non–singular matrix and the eigen values of A are 2 , 3 , -3 then the eigen values of A-1 are
If λ1 ,λ2 ,λ3 ....λn are the eigen values of a non–singular matrix A, then A-1 has the eigen values 1/λ1 ,1/λ2 ,1/λ3 ....1/λn Thus eigen values of A-1are 1/2, 1/3, -1/3
If -1 , 2 , 3 are the eigen values of a square matrix A then the eigen values of A2 are
If λ1 ,λ2 ,λ3 ....λn are the eigen values of a matrix A, then A2 has the eigen values λ12 ,λ22 ,λ32 ....λn2 So, eigen values of A2 are 1, 4, 9.
If 2 , - 4 are the eigen values of a non–singular matrix A and |A| = 4, then the eigen values of adjA are
If 2 and 4 are the eigen values of A then the eigenvalues of AT are
Since, the eigenvalues of A and AT are square so the eigenvalues of AT are 2 and 4.
If 1 and 3 are the eigenvalues of a square matrix A then A3 is equal to
Since 1 and 3 are the eigenvalues of A so the characteristic equation of A is
Also, by Cayley–Hamilton theorem, every square matrix satisfies its own characteristic equation so
If A is a square matrix of order 3 and |A| = 2 then A (adj A) is equal to
The sum of the eigenvalues of is equal to
Since the sum of the eigenvalues of an n–square matrix is equal to the trace of the matrix (i.e. sum of the diagonal elements) so, required sum = 8 + 5 + 5 = 18
If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal to
Since the product of the eigenvalues is equal to the determinant of the matrix so |A| = 1 x 2 x 5 = 10
If the product of matrices
is a null matrix, then θ and Ø differ by
If A and B are two matrices such that A + B and AB are both defined, then A and B are
Since A + B is defined, A and B are matrices of the same type, say m x n. Also, AB is defined. So, the number of columns in A must be equal to the number of rows in B i.e. n = m. Hence, A and B are square matrices of the same order.
If A is a 3-rowed square matrix such that |A| = 2, then |adj(adj A2)| is equal to
then the value of x is
Inverse matrix is defined for square matrix only.
A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is
Select a suitable figure from the four alternatives that would complete the figure matrix.
In each row (as well as each column), the third figure is a combination of all the elements of the first and the second figures
For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:
Matrix D is an orthogonal matrix The value of B is
For orthogonal matrix
From linear algebra for Anxn triangular matrix . DetA = The product of the diagonal entries of A