a)
So that
So that
Meaning
So that
We and this must hold for all
Which is only possible if
b)
Then
Which means
Im not understanding why you let t=0 and t=1 can you explain? thank you! 2. Consider...
Please answer if only 100% sure. Thank you so much 2. Consider the set V = span {v1 = (1,0,2), v2 = (2,1,2)). (a) For each choice of numbers for a and b, the set of points of the form (3,2, a) + t(b,-1,4), ter, is a line L in R. In set notation: L= {(3,2,a) + t(b, -1, 4) € R3 TER} Find all values of a and b, if any, for which the line L is contained in...
Find the projection of vector on the convex linear combination? Thank You! 3 Let t = span{f}]}._ = span{{{1}+{[1]}, and let S be the set of convex linear combinations of | and [2]. For i = [!] find (a) proje V. (b) proj, v. (c) projs 7.
Please solve using matrices and not equations. Thanks. 2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
please give the correct answer with explanations, thank you Let S {V1, V2, V3, V4, Vs} be a set of five vectors in R] Let W-span) When these vectors are placed as columns into a matrix A as A-(V2 V3 r. ws). and Asrow-reduced to echelon form U. we have U - -1 1 013 001 1 state the dimension of W Number 2. State a boss B for W using the standard algorithm, using vectors with a small as...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
please show work. thank you 1. Consider the vectors: (a) Determine if b = 0 is a linear combination of a, a, and a bi (b) Determine the set of values of b1,b2, bg such that b2 is not a linear combination of a as, and 2. Explain why the nullspace of R the same as that of M, where R is the RREF of M.
please show work, im having trouble to do it. Thank you Math 130 -Section 1.7 Solving Inequalities 1. Let S-(-3,-1,0, v2.4), Determine which elements of S satisfy the inequality. (a) 3r + 1< 4 (b) r2-32 2 2. Solve the linear inequality. Express the solution using interval notation and graph the solution set. (a) 4 - 13 > 5 t13 (b) -2r +5 s 9 - -S +13 2x44 2,00) (o (c) 5 3x-4S 14 t> (P) 923x 418 32x26...
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the line integral S ry ryds. 1/V2. 1/2, V2, 0,