. Consider the set of vectors in R³:It follows that(A) S is a basis for R³(B) S is linearly dependent(C) The system of equations(D) S is not a basis for R³(E) S spans R³$-{G).0)}.S =311 2-2 73 1x =ab has a solution forсc) ER³s Reserved.uogueiph.ca.

Answered: Image /qna-images/answer/74339373-9ed0-4eda-97b7-1ceb1e4b18dd.jpg

Answered: . Consider the set of vectors in R³: It…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a) W is the set of vectors of the form (3s, -2s, s). (b) W is the set of vectors of the form (t – 2, 0,6 – 3t). (c) H is the set of vectors of the form (2b, a, 3b) (d) H is the set of vectors of the form (-b+ 2c, b, 4c),
Show that the vectors p1(x) = a + bx and p2(x) = c + dx are linearly independent in P1(R) if and only if the constants a, b, c, d satisfy ad − bc ≠ 0
5: The vectors v = [1 2 9]" and w= [2 4 18] are linearly independent vectors. True False
4] Show that the following sets of vectors are linearly dependent in R3. (c) {{5, 2, -3), (3, 0, 4), (-3, 0, -4)} (d) {{1, 1, 1), (2, 2, 2), (0, 1, 5)}
1.
Q.3 Determine a scalar e so that the vectors a- and b- are orthogonal.
If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = 1 -7 -25 -3 12 39 and b = -4 3 Find a single vector x whose image under T is b. 3 -A X = Is the vector x found in the previous step unique? O A. No, because there are no free variables in the system of equations. O B. No, because there is a free variable in the system of equations. O C. Yes, because there is a free variable in the system of equations. O D. Yes, because there are no free variables in the system of equations.
Answer the following questions: (a) () Find the 12-norms of the vectors, x = (1,2,3)™ and y = (1,2,3)T and y = (9, 11, 13). (b) ma Show that the set, ( is orthonormal. T T 5-{(2,-1,0)", (1,2-5), (2.4.2)"} 2, 4, = S = T 1 30 √24 (c) i- Let f(x) sin x and consider co = 4, x1 9 and x2 = = after rounding. Now, Find the polynomial using Least Square Approximation for n = 1. -6. For f(x) take up to 3 decimal places
3. Let T = 1 7 W= 1 and x = 0 (a) Are vectors u, V, and w linearly independent? (b) Do u, v', and w span the entire R³? (c) Do u, v', and w form a basis of R³? abc po
Which of the following vectors are linearly independent? A) [1 2 3] [4 5 6] [7 8 9] B) [2 2 -1] [4 0 2] [0 6 -1] C) [1 2 3] [2 4 6] [3 4 5] D) [1 3 -2] [4 7 1] [3 -1 12] E) [1 2 1] [9 5 2] F) [3 5 2] [1 7 6] [2 5 31 G) [2 5 2] [1 6 6] [4 H) [-9 5 2] [1 -5 6] 12 5 -91 17 1 ol 10 41

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. Consider the set of vectors in R³: It follows that (A) S is a basis for R³ (B) S is linearly dependent *- {(→).()}. S = 3 3 1 2 (C) The system of equations -2 7 x = 3 1 (D) S is not a basis for R³ (F) S spans 3 a b has a solution for C Reserved. ER uoguelph.ca.