Consider the basis B= {1, x+x2, 2x2-1} for the vector space P,. The coordinate vector of the polynomial p(x) = 7 + 5x + 4x2 relative to B is B

W is a subspace of R4 consisting of vectors of the form. Determine dim(W) when the components of x satisfy the given conditions.

Find an othonormal basis of the subspace that is the set of solutions to the following system:

Consider matrix A = Answer: 0 1 (₁2) G -1 2 and vectors x = (¹2₂) and y = (1). . Calculate matrix B = (A – AT)² and vector w = Bx. Then, evaluate the scalar product w · y. [Please enter your answer numerically. You will be marked correct as long as what you enter is within 0.5 of the correct answer.]

Consider the vector space P, of all polynomials of degree = a, a2+b, b2 , then the magnitude of p(x)=2+1.7x equals: Answer: