(1 point) Let -6 -12 9-161 A=14 6-6 Find a non-zero vector in the column space of A. (1 point) Let -6 -12 9-16...
(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...
9. O-12 points LarLinAlg8 4.6.021 Find a basis for the column space and the rank of the matrix. (a) a basis for the column space (b) the rank of the matr O-2 points LarLinAlg8 4.1.019. 10. (-2,-1, 2). Let u (1, 2, 3) and v Find u- v and v- u. u-v V-u nment Poaross
9. O-12 points LarLinAlg8 4.6.021 Find a basis for the column space and the rank of the matrix. (a) a basis for the column space...
Q2. (20 points) Given A = 62 31 find a non-zero column vector u = } such that Au = 3u -3)
(1 point) Let 1-13 153:) -4 -6 6 9 Find a basis for the null space of A. { (1 point) Find the value of k for which the matrix 8 10 -9 A= 4 -4 -9 6 k has rank 2. k=
(1 point) Find a non-zero vector x perpendicular to the vectors ✓ : 2 and ū -4 -2 =
(1 point) Find a non-zero vector x perpendicular to the vectors 1 3 -10 ✓= and ủ -3 2 2 =
(1 point) Find a basis for the column space, row space and null space of the matrix 8 -4 4 -2 6 2 -5 -4 1 -1 -3 2 -1 Basis of column space: {T Basis of row space: OTT {{ Basis of row space: Basis of null space:
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A)
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
(1 point) Let 4 4 -4 3 -2 A-14-3-2 4 -2 5 3 5 Give a non-zero vector in the null space of A
r01234 A 0124 6 oo012 Let N(A) be the null-space and C(A) be the column space of A. Find a basis for each of the four fundamental subspaces C(A), N(A), (C(A)) and (N (A))
r01234 A 0124 6 oo012 Let N(A) be the null-space and C(A) be the column space of A. Find a basis for each of the four fundamental subspaces C(A), N(A), (C(A)) and (N (A))