Linear Algebra Answers

write the list for the SBN:A={x:xs greater than or equal to -3, x is an element of the set of integers}

Two of the eigenvalues of a 3*3 matrix A are 2 and 3 and the determinant is 48. Find the third eigenvalue and the trace (A)

Given that matrix A has 1has the eigenvalue with the corresponding eigenvector (1,-3) and 5 as the second eigenvalue with (1,1) as the corresponding eigenvector. (I) find the matrix A (Ii) D the diagonal matrix such that P^-1 AP=D

Let a, b, c, d be a set of real numbers, show that a²+b²+c²+d²=1

If the matrix of

a²-1 ab ac ad

ba b²-1 bc bc

ca cb c²-1 cd

da db dc d²-1

equal to zero.

Let a, b, c, d be a set of real numbers, show that a²+b²+c²+d²=1

If the matrix

a²-1 ab ac ad

ba b²-1 bc bc

ca cb c²-1 cd

da db dc d²-1

equal to zero.

Let V=R. Define addition and scalar multiplication by a+b=4a+4b. Show whether addition is both commutative and associative.

If dim V

T be a linear transformation on V and A and B be two ordered bases for V and A is the matrix of T relative to A and B is the matrix of T relative to B then prove that A and B are similar.

If T and S are similar then prove that T^(2) and S^(2) are also similar .Further if T and S are invertible then prove that T^(-1) and S^(-1) are also similar.

Suppose T € L(R^2) is defined by T(x;y) = ((3y; x). Find the eigenvalues of T.