Q1 Vectors 3 Points Q1.1 1 Point For what value(s) of a and b are the a - b 4 vectors u = 2 and b = atb equal? The value of a : Enter your answer here The value of b : Enter your answer here Save AnswerQ12 1 Point Determine the head of the vector 17 = [52] whose tail is (3, 2). The alt-coordinate Enter your answer here and the y-coordinate Enter your answer here Save Answer Q13 1 Point Determine the components of the vector PQ from the point P = (1, 2) to the point Q = (3,5). The alt-component Enter your answer here and the y-component: Enter your answer here Save Answer Q2 Vector Spaces 3 Points For operations 69 and (9 defined on a set V of elements. We say these operations are closed in V,if for any 11 and v elements in V, then 11 69 v or u G) v in the V. Q2.1 1 Point Consider the set V of all 2 X 2 diagonal matrices of the form for any a, b E R. Let EB be addition of matrices and (D scalar multiplication of matrices. Is V closed under ? 0 Yes O No Is V closed under 6)? 0 Yes O No Save Answer Q22 1 Point Consider the set V of all 2 X 2 invertible matrices. Let be addition of matrices and (E) scalar multiplication of matrices. Is V closed under 63? 0 Yes O No Is V closed under (9? 0 Yes Save Answer Q23 1 Point Consider the set V of all polynomials of degree exactly 2, Le. polynomials of the form p(:c) = 0,332 + in: + c, witha,b,cERanda70,anda:ER. Let be the usual addition of real numbers and Q the usual scalar multiplication of real numbers d (D p(33) = d(a:1:2 | 5:13 l c) for every d E R. Is V closed under 69? 0 Yes O No Is V closed under (9? Q3 Subspaces 1 Point Which of the following are subspaces of the set of all 2 x 2 matrices? C] The set of 2 X 2 diagonal matrices. C] The set of 2 X 2 invertible matrices. C] The set of 2 X 2 symmetric matrices AT 2 A. [:J The set of 2 X 2 lower triangular matrices. [:l The set of 2 X 2 nonsingular matrices. [:J The set of 2 X 2 upper triangular matrices