For the given matrix A, find k such that Nul A is a subspace of and find m such that Col A is a subspace of 1-2 11) A = 0 -4 -1 -3 3 -5 6 5 A) k = 5, m = 2 B) k = 5, m = 5 C) k = 2, m = 5 (D) k = 2, m = 2

Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not a…

Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

A:

Q: Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9.…

A:

Q: give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a.…

A:

Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

A:

Q: The vector a can be projected onto the subspace spanned by uj and 02. This resulting projection of ā…

A: We are given that a→=-1-1011, v1→=1825,  v2→=20-19-4 and vector  a→ is projected onto the subspace…

Q: Let fn : [0, 0) –→ R be given by fn(x) = e-na. (a) Find the pointwise limit f of the fn. (b) Show…

A: Answer

Q: Let Hspan {(-3,-1,-2), (17, -1, 10), (-5, 0, -3)}. A basis for the subspace HCR³ is { vector

A:

Q: a) {(1,-1,2),(5,-4,1),(7,-5,-4)}. b) {(1,3,3),(1,5,-1),(2,7,4),(1,4,1)}.

A: To Determine a basis for the subspace of Rn spanned by the given set of vectors by usingthe concept…

Q: Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The…

A:

Q: Determine if all polynomials P = ao + a,x + a,x² + a3x³ , with ao, a1, a2, az integer, is subspace…

A:

Q: Let V be the subspace of P^4 spanned by B = {1,x^2,x^4}. Create a chnage of basis matrix Cd,b if D =…

A:

Q: 21 3 Find a basis for the subspace of R³ consisting of all vectors 22 such that 61 - 7x2 - 4x3 = 0.…

A:

Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

Q: Question 1) The dimension of the subspace of P3 consisting of all vectors of the form at³ +bt² + ct…

A: (1) Given: at3+bt2+ct+d, b=2a-5d, c=d+4a ∴abcd=a2a-5d4a+dd            =a1240+d0-511 Therefore the…

Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

Q: Find a basis for the subspace of R4 determined by the equation 2x-3y+4z w = 0

A:

Q: Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај,…

A:

Q: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

A: To Find: Basis for the subspace of R2  of the form (a,b,c,d) such that c=a+7b and d=a-6b

Q: Let S be the set of all real 2x2 matrices whose rows are orthogonal vectors. Show whether S is a…

A: To determine whether ( S ) is a subspace of (Mat2x2​(R)), we need to check if it satisfies the three…

Q: Find a basis for the orthogonal complement of the subspace of R spanned by the vectors. v1 = (1,5,…

A:

Q: Find a basis of the subspace of IR defined by the equation 871 - 7x2 - 4x3 = 0. Basis:

A:

Q: There are four vectors (1,a,b,c), (1,1,1,1), (1,2,3,1), (3,4,5,3). If the vector space (subspace)…

A:

Q: Let A be any 5x7 matrix for which the col(A) has dimension 3, calculate: the nullity(A), and, state…

A:

Q: Suppose that V is a that has subspaces of U and W. Furthermore, suppose that {u¹, u2} is a basis for…

A: Linear Independence: Since  u1​​,u2​​ and  w1​​,w2​​ are bases for their respective subspaces U and…

Q: (a) Write one of the four vectors -3 3 2 8 as a linear combination of some or all of the others. (b)…

A: Given: u→=-312, v→=-125, w→=138 and x→=-7-1-4 To find: a) One vector is linear combination of some…