9. Find the dimension of each of the following vector spaces (a) The vector space of...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all lower triangular 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, c, 2a + 3b – 3c) (which is a subspace of R4).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of R).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R).
Solve 9.1 (iii) Problems 9.1. Find the dimension of the following spaces spanned by all (i) m x n matrices, and give a basis for this space (ii) n x n upper triangular matrices
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
no calculator please 1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R®). 2. (12 pts) Given the matrix in a R R-E form: 1000 3 0110-2 00011 0 0 0 0 0 (a) (6 pts) Find rank(A)...
8. Let Maxn denote the vector space of all n x n matrices. a. Let S C Max denote the set of symmetric matrices (those satisfying AT = A). Show that S is a subspace of Mx. What is its dimension? b. Let KC Maxn denote the set of skew-symmetric matrices (those satisfying A' = -A). Show that K is a subspace of Max. What is its dimension?
8. What is the dimension of the vector space consisting of lower triangular 5 x 5 matrices? Make sure to show how you obtained your answer.
(1 point) Let Ps be the vector space of all polynomials of degree at most 3, and consider the subspace 11 = {r(z) e Pal p(1) = 0} of P3 a A basis for the subspace H is { 22x+12x^2-x-1 Enter your answer as a comma separated list of polynomials. b. The dimension of His 3 (1 point) Find a basis for the space of symmetric 2 x 2-matrices If you need fewer basis elements than there are blanks provided,...