2. (4) Let W = span{(1,1,1), (-1,1,0)). Let v = (1,-1,2). Find the decomposition v =...
(20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b (c) Find the solutionx to the least square problem for Ax = b. (d) What is the vector in W that best approximates b? (20) Let W be spanned by (1,1,0)7 and (1,-1,2)T in R3x1 Find the projection matrix from R3x1 onto W (a) (1,1,1)7 in W? (b) Is the vector b...
Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)
Let B (1,1, , (1,1,0), (2,0,0))} and = {(0,0,1), (0,2,3), (1,1,1)} be bases for R3. Find Pa and P Let B (1,1, , (1,1,0), (2,0,0))} and = {(0,0,1), (0,2,3), (1,1,1)} be bases for R3. Find Pa and P
4. Find the orthogonal decomposition of v with respect to W A. 1 1 V= 4 -2 3 ,W = span 2 :1) 7 1 B. 2 1 1 1 0 V = W = span (0 5 6 0 1
4. Find the orthogonal decomposition of v with respect to W A. --[ : ) ----([1][:] B. 0 0 l W span ( 5 )
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
Let T: R3 R3 be a linear transformation such that T(1,1,1) = (2,0,-1) T(0,-1,2)= (-3,2,-1) T(1,0,1) = (1,1,0) Find T(-2,1,0). a) (10,0,2) b)(3,-1,-1) c) (2,2,2) d) (-3,-2, -3) Your answer MacBook Air
Let W = span{ (-2, 1; 2,0), (4,0-5, 2)] the Groun - Student Produrt to find an enthonormal basis for W The dimension of wt, the orthogonal complement of w.is basis from (a), either before or after normalizing projw (1,1,1,). be your to find
Consider the subspaces U=span{[4 −2 −2],[10 1− 4]} and W=span{[3 −4 −1],[10 2 −2]}.Find a matrix X∈V such that U∩W=span{W}.
2 = -4 and x3 = 0, with p = 1 and W = span{x1, X2, X3}. 4) Let x1 = -2, X2 3 (a) W is a subspace of R". What is n? (b) Find a basis for W. (c) Isp EW? (d) Give a geometric description of W.