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Let V1 = (1,2,0)^T, V2 = (2,4,2)^T, and V3 = (0,2,7)T and A = [V1,V2,V3] 5) (20 points) Let vi = (1,2,0)T, v2 = (2,4, 2)T and v3 = (0, 2.7)T and A- [v1, v2, v3 a) Find an orthonormal basis for the Col(A) b) Find a QR factorization of A. c) Show that A is symmetric and find the quadratic form whose standard matrix is A
Please show work Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that (V1, V1) = 51, (V2, V2) = 638, (V3, V3) = 36, (w, V1) = 153, (w, v2) = 4466, (w, V3) = -36, then W = _______ V1 + _______ V2+ _______ V3.
Let H = Span{V1, V2} and K = Span{V3,V4}, where V1, V2, V3, and V4 are given below. 1 V1 V2 V4 - 10 7 9 3 -6 Then Hand K are subspaces of R3. In fact, H and K are planes in R3 through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. W= [Hint: w can be written as C1 V2 + c2V2 and also as c3 V3...
Linear Algebra 6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2 = (-2,3,1,0), V3 =(4,-5, 9,4), V4 = (0,4,2, -3) V5 = (-7, 18, 2, -8) that forms a basis for the space spanned by these vectors. (b) Use (a) to express each vector not in the basis as a linear combination of the basis vectors. (c) Let Vi V2 A= V3 V4 Use (a) to find the dimension of row(A), col(A), null(A), and of...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Let H = Span{V1, V2} and K = Span{V3,V4}, where V1, V2, V3, and V4 are given below. Then H and K are subspaces of R3. In fact, H and K are planes in R3 through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. w= _______
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, V1 + V2, 2v1), v = (2,3,0), w = (-9, -3, 6) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.) Use the function to find the image of v and the preimage of w. TIV3, va) = (v2v2 -...
Homework: Section 4.1 Score: 0 of 1 pt 4.1.13 3 4 11 Let v1 0 , V2|1 V3 3 and w= 1 1 4 10 Is w in {v,, v2, v3}? How many vectors are in {v,, v, V3}? b. How many vectors are in Span{v, V2, V3}? c. Is w in the subspace spanned by (v,, v2, V3)? Why? a a. Is w in {v, V2 V31? O A. Vector w is in {v,, v2, V3} because it is...