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X = [X1, X2, ... , Xn] is an n — tuple non — zero vector. Then n x n matrix V = VX
Consider a non — homogeneous system of linear equation represented mathematically an over determined system. Such a system will be
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
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 A is a non scalar non identity idempotent matrix of order n≥2. the minimal polynomial mA(x) is
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
The rank of the following (n + 1 ) x (n + 1) matrix where a is the real number
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 statements is incorrect for an upper triangular matrix A = (aij)?