and Consider the subspaces X = U = span{ [4 4 -5],[1 -8 1]} W = span{ [0 4 -5], [-3 -4 -4]} of V = R¹X3. Find a matrix X E V such that Un W = span{X}. 1x3

Let S be the set of all real 2x2 matrices whose rows are orthogonal vectors. Show whether S is a subspace of Mat2x2 (R)

Find the dimension of the subspace Hof R2 spanned by

State the Fundamental Subspace Theorem and give an example of its application in the case of a 2 x2 matrix.