For which value of x will the matrix become singular.
A matrix is
is a 3 X 3 matrix over the set of
If A = , then A2 is
1 x n matrices are called
Let f(x) = x2 — 5x + 6 and A = then f (A) is equal
is called a
X = [X1, X2, ... , Xn] is an n — tuple non — zero vector. Then n x n matrix V = VX
A submatrix of the given matrix can be obtained by deleting
Consider a non — homogeneous system of linear equation represented mathematically an over determined system. Such a system will be
Two matrices A and B are said to be comparable if
Consider the system of equation A(nxn)X(nx1) = λ nx1 where, λ is a scalar. Let, (λi, xi) be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correct
If A = and B = then A x B =
Eigen values of a matrix S = are 5 and 1. What is the eigen values of the matrix S2 = SS?
If A is non - scalar, non - identity idempotent matrix of order n ≥ 2. Then, minimal polynomial mA(x) is
If 4X = then X
If A is a non scalar non identity idempotent matrix of order n≥2. the minimal polynomial mA(x) is
Since A is idempotent A2 = A
A2 - A = 0
mA(x) = x2 - x
If A = and B = then AB is a matrix of order
All the four entries of the 2 x 2 matrix P = are non - zero, and one of its eigen values is zero . Which one of the following statements is true?
In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vector
If D1, D2 are two diagonal matrices, then
Matrix multiplication is
The rank of the following (n + 1 ) x (n + 1) matrix where a is the real number
R2→R2−R1,R3→R3−R1,R4→R4−R1, and so on
Rank of matrix = 1
Multiplication of matrices E and F is G. Matrices E and G are as follows
Then, the value of matrix F is
The linear operator L(x) is defined by the cross product L(x) = b x X, where b = [0 1 0]T and X = [x1 x2 x3]T are three dimensional vectors. The 3 x 3 matrix M o f this operation satisfies L (x ) = Then, the eigen values of M are
Which one of the following is not an elementary operation?
Which one of the following statements is incorrect for an upper triangular matrix A = (aij)?
Mark the correct definition of rank of a matrix
The rank of matrix a, b, c, being all real, is 3 if
Two matrics Aand B are said to anti — commute if