Which of the following sets of vectors form anorthonormal basis for R2?(a) {(1,0)", (0, 1)")5 12(b)13' 13(c) {(1,-1)".(1, 1)"}{(4)T(d)22' 2

We use the definition of orthonormal vector.

Answered: Which of the following sets of vectors…

Which of the following sets of vectors form an orthonormal basis for R?? (a) {(1,0)", (0, 1)") (b) (c) {(1,-1)".(1, 1)") T V3 2 2 (d)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: Prove that the vectors (1. 1. 0) (1 2 3) and (2. –1 5) form a basis for R3

Q: B = (1, x+1, x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of the…

A: The coordinate vector of v with respect to is given by such that .(a) Given .Comparing the…

Q: (b) The general fact that fcu++eUn]e== c\]j + .. + ca[vn]s allows for rewriting the equation above…

A: It is an important part of statistics. It is widely used.

Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

Q: Let 0.5 0.5 -0.5 0.5 -0.5 0.5 üz = -0.5 0.5 0.5 -0,5 -0.5 -0.5 Find a vector ig in R' such that the…

Q: 5. Do the vectors {(1, -2, 1), (2,-3, 1), (5, -8, 1), (-1, 1,2)} form a basis for R'? Provide a…

Q: (a) Suppose A=(S,+S) and B (S-S), Show that S = A + B A= A and B =-B (b) Suppose that A B, is a…

Q: 2 1. Find a basis for span(S), where S = -2 6.

A: Please see the explanation below

Q: 7. Let S = Show that span S = R' and find a basis for R' consisting of vectors from S.

A: Span of vector : Let us consider a vector space V then the set S is aid to be the span of V if the…

Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

Q: Consider the elementary basis vectors & € R¹ (column vectors). Show that the matrix eje +e₂e₂+...+ee…

A: Given that ei→∈Rn are elementary basis.We need to show that e1→e1→T+e2→e2→T+…+ek→ek→T has rank k.We…

Q: 1. Find the coordinates of vector w (1,2, 3) in the basis A which consists of T1 = (1, 1, 0), 72 =…

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the question does not make an…

Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

Q: s the set of the vectors (:). (2) 1 ) --(;) --() u2 4 U3 = 1 1 1 rthogonal? What is the expression…

Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: 3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị…

Q: (a) Given S={(1,-5,4), (11,6,-1), (2,3,5)} the set of vectors in R³. Determine whether (i) S spans…

Q: Be S = {v1 = (1, 2, 1), v2 = (2,9, 0), v3 = (3, 3,4)} a subset of R and T: R → R? T(v1) = (1,0),…

Q: 1 17. В %3D is an ordered basis of R². = , 2 find x. 3 (a) If the B-coordinate vector of a vector x…

Q: Let -0.5 0.5 0.5 -0.5 -0.5 0.5 , V2 , U3 -0.5 0.5 -0.5 0.5 0.5 0.5 Find a vector v4 in R' such that…

Q: Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for…

A: a)b)c)d)

Q: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

Q: 1. (a) Determine whether the following three vectors v, = (0, 3, 1,-1), v2 = (6, 0, 5, 1) and vz =…

A: Solution Given v1=(0,3,1,-1) v2=(6,0,5,1) v3=(4,-7,1,3) in R4 We need to find the linearly dependent…

Question

Which of the following sets of vectors form an
orthonormal basis for R2?
(a) {(1,0)", (0, 1)")
5 12
(b)
13' 13
(c) {(1,-1)".(1, 1)"}
{(4)
T
(d)
2
2' 2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Final Answer

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inner Product Spaces$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

-7 4 -4 4 Let T = 3 -7-4-1 -6 A nonzero vector with integer entries in the null space of T'is 00000
(b) Is the following set of vectors S basis for vector space V? Where (i) S = {(1,2), (0, 3), (1, 5)} and V = R? (ii) S = {(-1,3, 2), (6, 1, 1)} and V = R³ If not explain the reason.
Find a basis for the plane 4x + 3y + 5z = 0 in R³. |
5. Determine the courdinate vector of V =(8,-4,-12) velative to the basis S = {C,,1),(1,s,-3), (2,2,113
2. The vector x = H [13] vector [2]B = [8] A 1 B 2 3 D0 in R2 relative to the orthogonal basis B What is the value of a + b? {0-[-]} has coordinate
4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b=2i-j. Then the coordinates of vector u in the basis {i, j,k} are 2 3 (a) (b) (-1, 2,–3) (c) None of the above is true
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
Which of the following vectors are orthogonal to product inner product (21 27 -39)T (-7 -9 13)T (-2.8 -3.6 5.2)™ (35 15 -65)T 3 -2 ().(-)- 2 3 1 3 , using a dot-
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D