Linear Algebra Answers

Show that matrix A given below is skew-hermitian:


A=[0 -5-i -2+3i]

[ 5-i -3i -6]

[2+3i 6 6i ]

Show that the function omega = sin z satisfies the Cauchy-Riemann and Laplace
equations

Define covariant and contravariant tensors of rank two. What is the rank of a scalar
tensor? Show that the Kronecker delta function is a mixed tensor of rank 2

Identify the conic section whose equation is

5x^2-4xy+5y^2=4

Show that every eigenvalue of a unitary matrix is of unit modulus.

Define skew-hermitian matrix, orthogonal matrix and unitary matrix with an
example of each.

Find the orthogonal canonical reduction of the quadratic form
−

Suppose that A is a 3x3 matrix and that b is a 3x1 matrix. Assuming that
the matrix equation Ax = b has infinitely many solutions, write down all the possible
reduced row-echelon forms of the augmented matrix (A | b). You may use ‘*’ to
represent an unknown number.

Find two 2 x 2 upper triangular matrices C,D such that C and D are both
not diagonal, but CD is diagonal.

Let A = (-1 0 4)
6 3 2
2 5 6 3x3 then find
A/ Det(A)
B/ Cofactor of A
C/ adjoint of A
D/ Inverse of A