(a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1, –3, 2), (2, 1, -3) and (-3, 2, 1) linearly independent?

Q: Detexmine the Vectors are lineably independent -3 -3 6.

A: 2 vectors are given

Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

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Q: Q-4: a) Determine whether the vector (9,0,9) is a linear combination of the vectors (1,1,0),…

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A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given: Two nonzero vectors v and w, v can be decomposed into two vectors, one parallel to w and the…

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Q: Which of the following vectors are linearly independent? O None of these O (2,1,1), (1,3,2),…

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Q: w = (-2,0) , v1 = (-1,2), v2 = (4, –8) , vz = (-1,1). If possible, express w as a linear combination…

A: Let us assume -20=a-12+b4-8+c-11. So,               -20=a-12+b4-8+c-11⇒-20=-a+4b-c2a-8b+c⇒a=4b-2,…

Q: 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^4 are…

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Q: 5. Determine the value of a so that the vectors v = perpendicular. (a,3, -2) and v - (2, -2a, 1) are

A: Solve the following

Q: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

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Q: The vector (-1, 5, 3) is orthogonal to vector : Select one: О а. (0, 1, -2) O b. (-1, 1, -2) О с.…

A: Two non-zero vectors are orthogonal to each other if their dot product is equal to zero.

Q: Which option is the right? Two vectors are linearly dependent if: -They have the same address -They…

A: Two vector are linearly dependent if in linear combination of v1 and v2 , not all scalar are zero

Q: Let a = (-1; 3; 2) and b = (4; -2; 1). Find two unit vectors orthogonal to both a and b. Are the…

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Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

Q: The normal vector of x+2y-1-0 (0, 2) (2, -1) (1, 2) O (1, -1)

A:

Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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Q: Determine if the vectors , and are linearly independent.

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Q: Determine all values of the constant k for which the vectors (1, 1, k), (0, 2, k), and (1, k, 6) are…

A: We have to find the value of constant k for which the vectors are linearly independent.   According…

Q: Determine all values of the constant k for which the vectors (1,0, 1, k), (-1,0,k, 1), and (2,0,1,…

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

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

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: snip1

A: (a) Let the vector 123 be a linear combination of the vectors 103 and -11-3. Then we can find…

Q: и, %3 (1,2,1, — 4,1), и, 3 (1,2, —1,2,1), и, — (2,4,1, —5,0), и, — (1,2,3,—10, 1)

A:

Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given that : The statement : Given two nonzero vectors v and w, v can be decomposed into two…

Q: 6. We have two vectors: a =) and b= 8 What is the resultant of -a plus b? (

A: Given:     To find: -a + b

Q: a) Determine k so that the vectors (1,–1, k – 1),(2, k, –4) and (0,2 + k, -8) in R³ are linearly…

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

Q: 19. Find two unit vectors orthogonal to both (3, 2, 1) and (-1, 1, 0). Answer

A: Unit vector orthogonal to both a⇀, b⇀ is: ±a⇀×b⇀a⇀×b⇀

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

Q: 2. Show whether the set of vectors in R*is linearly independent. Justify your answer. (1, 1, 1,0),…

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Q: Determine all values of the constant k for which the vectors (1,1,k), (0, 2, k), and (1, k, 6) are…

A: We know that if three vectors are linearly dependent then one of them can be expressed as a linear…

Q: 5. (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors…

A: Explained below

Q: 1. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors (2,…

A: We need to find r.

Q: Which of the following sets of vectors in R' are linearly independent? (a) (-3,0,4), (5,-1,2),…

A: Linearly independent set: The set of vectors x1, x2, ..., xn in a vector space V is said to be…

Q: -2 is a linear combination of the vectors 4. For which value of k the vector u = 3 2 3 and v2 of the…

A: Given the given vectors are u=1-2kv1=30-2v2=2-1-5

Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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Q: Q. Is the set of vectors Linearly independent or not ? {1,0, 0, 1), (0, 1,0,0),(,1,1, 1) (1, 7,…

A: As per our guideline we are allowed to do 1 question at a time. Please post other question next…

Q: 7. Find the cross product of the vectors (a) u=(1,2,-3) v=(-4,1,2) (b) u = (0,1,- 2) v = (3,0, - 4)

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Q: Show that the vectors V, =(1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = (1, -1, -4, 0 ) and V, =(2, 1,…

A: Sind the determinant of the matrix whose rows are given vectors

Q: 24. Write a vector (-3, 22, -3) as a linear combination of the vectors (-1, 2, 3) and (0, 4, -3).

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Q: 1. Are the vectors (-3, 0, 4), (5, -1, 2) and (1, 1, 3) linearly dependent in R3? a. Yes b. No

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Q: a-(:) We have two vectors: a = and b= What is the resultant of -a plus b? (

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Q: Is the set of vectors Linearly independent or not ? [{1,0, 0,1),(0,1,0,0),(1,1,1,1),(1,1,1,0)]

A: The set of the vectors are linearly independent. Rewrite the set of vectors in the form of the…

Q: Q.5. Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V,…

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Q: Find the orthogonal projection of the vector a (-9,-8, 7) in the direction of the (-3,-5,-2). vector…

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Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

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Q: Find the vector equation of a plane a) passing through the point A(-1,2,-3) and parallel to the…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.