4. Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? -3 2 9 1000 4 2 -3 2 5 -3

a b 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B с 0 is a basis for H. 10 Find the coordinate vector of v = according to the basis, B.

U₁ = 4 #0-0 -2,1₂ = and и3 = -32 Note that u₁, ₂ and 3 are orthogonal. V = Given v = 4 -0₁ 2 find the coordinates for v in the subspace Wspanned by 4 4 4 U₁ + -8 -8 U₂ +1 U3|

For the subspace below, (a) find a basis, and (b) state the dimension. 6a + 12b 2c 9a - 3b - 3c - 12a + 5b + 4c - - 3a + b + c : a, b, c in R a. Find a basis for the subspace. A basis for the subspace is . (Use a comma to separate vectors as needed.) b. State the dimension. The dimension is 2.

Suppose a subspace is spanned by the set S of vectors shown. Find a subset of S that forms a basis for the subspace, using the method of transforming a matrix to echelon form, where the columns of the matrix represent vectors spanning the subspace. GOL S= A basis is -3 16 20 What is the dimension of the subspace?