c) If A is a 5 x 4 matrix, what is the largest possible dimension of the row space of A? If A is a 4 x 5 matrix, what is the largest possible dimension of the row space of A? Explain Q2) Find the coordinate vector [x]g of x relative to the basis B={b1, b2}: bị = [7].b, = [],x = [ Q3) Use the inner product < p,q >= a,bo + a,b̟ + azbz to find < p,q >,llp||, d(p, q), and then find the angle between them for the polynomials in P2 if p(x) = 1 – x + x², and q(x) = x – 3x². Q4) For the following functions f(x) = e*,g(x) = e¬* in C[-1,1), find < f,g >,|\f|I, d(f,g), and then find the angle between them for the inner product. (x) dx Q5) Let W be the subspace spanned by the u's. Show that {u,,Uz} is an orthogonal set of vectors then write y as a sum of a vector in W and a vector orthogonal to W. y = (-1,4,3)',u, = (1,1,1)', uz = (-1,3,–2)'

Let u and v be column vectors from Rn and define A = I + uvT, where I E Rnxn is the identity matrix. What is the operation count for producing matrix A.

Find a and that solve the vector equation: a) 1 13 a (²) + ² ( ₂ ) = (₂3) 3 29 Suppose the above equation is expressed as Ax = b with x = the coeffieints of the equations in one matrix form as (Ab)= Rows: 2 Columns: 3 (²). Express

Find a and that solve the vector equation: Suppose the above equation is expressed as Ax = b with x = coeffieints of the equations in one matrix form as (Ab)= Rows: 2 Columns: 3 b) c) d) 21 a (²) + ^ ( ;) = (²1) B α= B = Complete the missing column of the following matrix derived by doing row operation of the augmented matrix in a): 1 -2 (²). 0 1 Express the