Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two perpendicular vectors each of unit length, then C is an orthogonal matrix. Hint: Find CTC.

Is w in the Column Space of A?

Define 0 1 B. - 13 V3 = 0 (Here, a, b, c, d are some unknown constants.) Assume that v3 is nonzero and is orthogonal to both vi and v₂. Also, let A be a 2 x 4 matrix whose row vectors are v₁ and v2, that is, V1 = (a) v3 is in Col(A). (b) v3 is in Nul(A). (c) v3 is in Row(A). A = V2 = 1 -1 1 0 -1 0 1 Mark each of the following statements as: (i) must be true, (ii) must be false, or (iii) may or may not be true.

2 Consider the matrix A = and the vector u = Let B = (A – A")2 and define vector v = Bu. If v = , write 1 down the value of vị. [Please enter your answer numerically in decimal format.