Answered: Problem 23. Determine if the following…

Problem 23. Determine if the following vectors are independent or dependent (a) the vectors are (1,3,2), (2, 1,3), and (3,2,1). (b) the vectors are (1, -3,2), (2, 1, -3), and (-3,2,1).

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: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

A: Solution :-

Q: Given the vectors v=[-1. 2, 4] and w=[0. -3, 1], which vector is perpendicular to both v and w? A…

Q: 3. Determine if the sets of vectors given are LI or LD and explain how you know. a) {(3,4),…

A: Here we apply theorems from linearalgebra.

Q: skip the first 3 thank you

Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: is the sum of 2 vectors with components and . What is a?

A: To find the value of a, you can use the properties of vector addition.Given that the sum of the…

Q: I have the following vectors, I have a problem with understanding why one becomes 'a+b' and the…

A: Vectors are geometric objects with both magnitude and direction. We will consider two vectors, a and…

Q: Suppose the equation ax + by = c corresponds to the vector (a, b, c). To what equation will…

A: Given that:The equation ax+by=c corresponds to the vector ⟨a,b,c⟩. (1).The given vector is:…

Q: 1] Determine whether the first vector is a linear combination of the other vectors. (c) (-1, 15);…

Q: (4,6) V2 = (-3, -6) V3 = (-8, 4) V4 = (10, ニ

Q: Please help

A: Step 1: Concepts and formulas. Step 2: Solution of first question. Step 3: Solution of second…

Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

Q: Write each vector as a linear combination of the vectors in S. (Use s, and s2, respectively, for the…

Q: Suppose the polynomial ax² + bx + c corresponds to the vector (a, b, c). 2 To what polynomial will…

A: ConclusionIn the context of the given problem, where vectors correspond to the coefficients of a…

Q: 15. Which is the component form of the vector shown? -2- * (1, 2) -4 (-5, -3) O (4,-7) O (7.-4)

A: This question is related to vectors, we will solve it using given information

Q: Which of the following sets of vectors are linearly independent? A. (4, 8,-5), (-9, -4, -6), (-13,…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: For the following three vectors are given in Cartesian coordinates: A₁ = [-4,3], A₂= [13,5], and A3…

A: The given vectors A1=-4, 3, A2=13, 5, and A3=12, 13. We have to find the values of a) A1, A2, A3 b)…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given : The given set is S = {(2, -1, 3) , (5, 0, 4)}. To find : We have to write the following…

Q: Use a grid and draw arrows to represent the following vectors. You canchoose any starting point you…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given,S = { (2, -1, 3), (5, 0, 4) }To find: the vector as a linear combination of the vectors in S.…

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Question

Problem 23. Determine if the following vectors are independent or dependent:
(a) the vectors are (1,3,2), (2, 1,3), and (3,2,1).
(b) the vectors are (1, -3,2), (2, 1, -3), and (-3,2,1).

Expert Solution

Step 1

To find- The following vectors are dependent or independent.

Concept Used-

If the value of the determinant of the matrix form of the given vector is zero, then the vectors are linearly dependent.
Otherwise, the vectors are linearly independent.

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

-2 - (+) (9) (-:-) and b = 2 Let a = What is a|²|b²+|a.b|²? 0 be two vectors.
Determine whether each vector can be used as a primary combination of vectors in S. Please write in alphabetical words
How do you know if three vectors are on the same line? (when they are on the same line we call them co-linear) If when you add them up, you get a constant If they are the same. If they are different. If each is a multiple of the other one. If you multiply the first one by 7 you get the second one and when you multiply the second one by your age, you get the third one for sure.
Show that the column vectors (1,1,2,4), (2,-1,-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are linearly dependent.
For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and (3,13,-3)?
Can 5 = (7,14,0) be written as a linear combination of vectors from the set {(1,-2,-1), (0,1,2). (3,–1,0)} ? If yes, clearly show how the coefficients are calculated (trial and error will not be accepted). If no, then explain why not. Determine with explanations and calculations whether the set {(-2,3,0). (1, –1,2), (0,3, 2)} is linearly independent.
If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?