Suppose A is invertible and orthogonally diagonalizable. Explain why A–1 is also orthogonally diagonalizable.

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, ... are not vectors but are entries in vectors. T(x1 X2 X3) = (*1 -2x2 +5x3, X2 - 9x3) A= (Type an integer or decimal for each matrix element.)

Find a basis for the vector space of all quadratic polynomials p(x) = ax²+bx+c, that satisfy p(−1) = 0.

Find a vector that spans the kernel of the following matrix: [ 1 0 2 4 ][ 0 1 -3 -1 ][ 3 4 -6 8 ][ 0 -1 3 4 ]