Linear Algebra Answers

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

Find the Square matrix M order of two such that M square of 2 - 2M= (-1 0) 2x2

6 3