The vectors -2 -4 u = -3 v = -2 w = -12 2 -1+ k 16 are linearly dependent if and only if k = 7

Q: For which value of z the set of vectors is a linearly dependent set in R2? 3. Select one: -2 3. none…

A: Option A is correct option. x= -2

Q: Write a vector equation that is equivalent to the given system of equations. X2 + 5x3 = 0 5x1 + 6x2…

A:

Q: For each of the following vectors b e R*, decide whether b is a linear combination of -1 -2 , and v3…

A: Given vectors are  v1=101-2,v2=0-101,v3=1-210 for given b we have to find if the b is linear…

Q: (b) x1 + x2 + 2x3 = 5 + x3 = -2 2x1 + x2 + 3x3 = 3 %3D X1 %3D %3D

A: We see from the given system that, if we add first two equations, we will get the third equation.…

Q: Given trna -2 0. 1. -1 -4 0. 1 0 2 -1 -1 1 3 -2 write -4 as a linear combination of the vectors -1…

A: We want to write vector in linear combination of given vectors.

Q: Which of the following sets of vectors are linearly independent? OA. B. -1 4 C. -4 -2 ELELEL 9 -6 2…

A:

Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: 15 |ム=() -40 -30 -20 -10. -5 10 10 -10 15 (8)

A: We have,  x1=-5, 5 and x2=2,-2 This can be done as follows:

Q: 12 2 Determine if the pair of vectors v₁ = 3 V₂ = =-3 are orthogonal. -5 3

A: We have to find whether the given two vectors are orthogonal or not?

Q: The zero vector 0=(0, 0, 0) can be written as a linear combination of the vectors v1, v2, and v3…

A: We need to find solution to the linear equations system.

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: For which real values of A do the following vectors form a linearly dependent set in R³? m = (A.-)…

A:

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: Write down all of the solutions (if any) to the following system of linear equations. Give your…

A:

Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: Let -16 -4' V1 16 and w = 43 Is wa linear combination of V1 and V2? Fill in the coefficients of the…

A: Given that:v1=4-5-1, v2=-16163, w=-44438

Q: Which of the following sets of vectors are linearly independent? 2 - 4 A S = 8. | 1 -3 B S = -1 -3…

A: To determine linearly dependent or independent, we would find the determinant for all the options…

Q: Find a value of k such that the given vectors are linearly dependent [ -2 4+ k 4 ,X2 = 2 X1= ,X3 =…

A:

Q: If --0--0---0 1 and v3 = 0 then the vectors V1, V2, and v3 are linearly dependent. Select one: O…

A:

Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: Q6:- A/ Show that the vectors A. (BxC) B.(CxÃ)=C.(AxB), if the vectors A= 31-j+2k B=21+j-k C= i-…

A:

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

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

Q: The vectors -5 3 u = 16 v = -9 w = 11 31 3+k -23 are linearly dependent if and only if k = 3

A:

Q: The vectors 3 -4 u = -7 = 12 w = -8 -23 + k are linearly independent if and only if k #

A:

Q: The zero vector 0 = (0,0,0) can be written as a linear combination of the vectors v1, v2, and v3…

A: Given that (0,0,0) = 0v1+0v2+0v3 is one way of writing in a trivial way the vector 0.

Q: In a standard Cartesian coordinate system a vector, R, has an x-component of + 5.0 m and a y-…

A: In a standard coordinate system a vector R has an x- component of +5.0 m and a y- component of -4.0…

Q: If the vector v = v1 <=2 2 of v₁ = 05 2 -20 [E] -2 can be written as a linear combination -12 v=a1…

A: Substitute the vectors and then go ahead

Q: Which of the following sets of vectors are linearly independent? a){[-6,4]} b){[0,0], [-9,2]}…

A:

Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. -4 2 - 4…

A: Vectors are Linearly Dependent so it (two vector) can be written as a linear combination of third…

Q: (a) Show that if {ủ, v} is linearly independent then {2u – ở, ù + 37} is linearly independent. |

A:

Q: Write a vector equation that is equivalent to the given system of equations. X2 + 4x3 = 0 5x1 + 8x2…

A:

Q: For what values of h are the given vectors linearly dependent? -24

A:

Q: The following vectors 3 X= 2 2 12 +b 2 are linearly independent if and only if b

A:

Q: The vectors 4 -2 -2 2 12 -5+ k 4 are linearly independent if and only if k +

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

Q: 3. Explain why as n goes to infinity. the entries of the vector A" 2 go to infinity, while the…

A: To solve question 3 I will take the help of eigenvalue and eigenvector of a matrix because question…

Q: Consider 2 -6] -4 V1 = -5 1,v2 = -3,V3 = 2 15 h (a) For what values of h is v3 in Span{v1,v2}?…

A:

Q: For which real values of A do the following vectors form a linearly dependent set in R? »- (A-) 1,…

A:

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

A: Given: To find the value of k such that vector u=1-2k is a linear combination of vectors v1=30-2 and…

Q: For which vectors (b₁,b2, b3) do these systems have a solution? X1 b₁ 1 1 1 X1 HO-N-HD-B b2 and 0 1…

A:

Q: Solve for w where u (0,-1, 1, 1) and v (2, 3, 0, -1). %3D %3D w + 2v = -4u W =

A:

Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v,…

A:

Q: The vectors 3. w = 12 20 + k 15 nearly independent if and only if k +

A:

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

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

A:

Q: -- -4 1 -3 For A = -2 find the orthogonal vectors vị, V2 and v3 to be used in constructing the 3…

A: Given matrix is: A=-41-302-2003

Q: Which of the following sets is always linearly dependent? :{V1, V2} where the equation a1V1 + a2V2 =…

A: According to the given information, it is required to tell which of the following sets are linearly…

Q: For what values of h are the given vectors linearly dependent? -24 h Vectors are linearly dependent…

A: