Which of the following sets of vectors are bases for R? (a) (2, 1), (3, 0) (b) (4, 1), (-7, -8) (c) (0, 0), (1, 3) (d) (3, 9), (-4, –12)

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: Find the coordinate vector (v)s relative to the basis S={v,,V2,V3} for v = (2, 1, -2), if V= (2, 2,…

A:

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 of the following sets of vectors are bases for R³ O {(3,4,5)} {(3,1,-4),(2,5,6).(1,4,8)} None…

A:

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:

Q: Which of the following vectors is orthogonal to (1, −1, 1, −1)? A. (-1,1,-1,1)  B. (-1,-1,-1,-1) C.…

A: Let's find orthogonal vector.

Q: Which of the following vectors is the scalar multiple of z-(4, 3, -2) ? Ou- (-28, -21, -14) Ou-(-24,…

A:

Q: Which of the following vectors MUST be linearly dependent? here a,b,c,d,e,f,g,h,i,j,k & l are real…

A: The objective is to find that which of the vector must be linearly dependent It is given that…

Q: Which of the following sets of vectors are bases for R2? (а) (2, 1), (6, 0) (b) (5, 3), (—10, —9)…

A:

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

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

A:

Q: Find the terminal point Q of the vector v = 7i-j+3k given the initial point is P(-2, 3, 5) О (5, 2,…

A: In this question we have to find the terminal point of Q.

Q: . Which of the following is an orthogonal pair of vectors? A. (1, 0, 1) and (1,1,0) B. (1, 1, 0) and…

A: The vectors a and b are said to be orthogonal vectors if their dot product is 0.

Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

A:

Q: (2,1, –4,0), v = (-1,-1,2,2), and 19. Find two vectors of norm 1 that are orthogonal to the vectors…

A: We have to find the basis of these vectors, which are independent. A=2-131-12-425024~I4 and they all…

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

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: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

A:

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

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

A:

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

A:

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

A:

Q: The following three vectors are coplanar: (3,5,6), (6,10,12), (-3,-5,6) True False

A:

Q: Find the coordinate vector of v relative to the basis S = {v,, V2, V3} for R³. (b) v = (5, –12, 3);…

A:

Q: Prove that A•(AxB) =0. Note that A and B are vectors.

A: Prove that A•(AxB) =0. Note that A and B are vectors

Q: how that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

Q: 5. Determine whether vectors u =(2,-6,-5), v = (3,8, 18) and w = (8,-6,7) will form a basis for R³.…

A: Basis is very important in linear algebra. A basis set always contains linearly independent vectors…

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

A:

Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of 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: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

A:

Q: For what value or values of the constant u are the following vectors are linearly related and are…

A:

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: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

A:

Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A:

Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: The given vectors are: And, Let the coordinates of vector w be, Substitute the coordinates in…

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)

A:

Q: - Find the length of the vector -3v if v = (2, 3, -2, 1).

A: Givenv=(2,3,-2,1)-3v=(-6,-9,6,-3)

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

A:

Q: 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5)…

A: First we need to find the vector and then find the opposite components of it.

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

A:

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

A:

Q: Which of the following are orthogonal sets of vectors? (a){(1, -1, 2),(0, 2, -1),(-1, 1, 1)}…

A: The sets of vectors u, v, w are orthogonal if u·v=v·w=u·w=0. Let two vectors be defined as…

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Q3/ Determine whether the given vectors are orthogonal, parallel or neither: (1) u =(-2, 6, -4) , v…

A: Given that two vector u and v and prove that its orthogonal , parallel or neither.     Here i…

Q: Find all vectors u that satisfy the equation (1,1,1)×u= (−5,2,3).

A:

Q: Identify the vectors that are orthogonal to v = (1,2, 1) but not to w = (1,0, – 1). 口(-2,2,0) (-1,…

A: u and v orthogonal if u.v=0 i.e. let u=(x1,y1,z1) and v=(x2,y2,z2) then u.v = (x1 * x2)+(y1 *…

Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

A: