(a) Show that the vectors v1 = (1, 2, 3, 4). v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a linearly dependent set in R4. (b) Express each vector as a linear combination of the other two.

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A: We need to determine all the values of the constant a for which the vectors

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A: It is false.

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Q: 2 Write the vector x= as a linear combination of the vectors -1 1) u=0 |, v=| 1 w= 1 1 N O H O O

A: Consider x = au+bv+cw then 20-1 = a100+b110+c11120-1 = a+b+cb+cc On comparing the coefficients , we…

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Q: () (3) The vectors and are Select one: a. Linearly dependent b. Linearly independent

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Q: 9. Find all real values of c such that the vectors and are linearly independent.

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A: Linearly independent

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

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Q: 2 1 3. Show that that the vector u = |-5| is a linear combination of the vectors v1 = |-3 3 2 2 V2 :…

A: The given vectors are: u=2-53, v1=1-32, v2=2-4-1  and  v3=1-57 Vector u=2-53 is a linear combination…

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A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

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

A:

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

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

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Q: Determine whether the following vectors are linearly independent in R2:

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Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: Which of the following pairs of vectors are linearly independent? Ou= (1,0) and w = (0,2). Ou =…

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Q: ) Show that the three vectors vị = (1, 2, 3, 4), v2= (0, 1, 0, – 1), and v3 = (1, 3, 3, 3) form a…

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Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

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A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: v Are the following vectors linearly independent? Yes ,, No

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Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

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A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

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Q: Which of the following vectors are linearly independent? (2) (0) 21

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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:

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Q: Determine if the given vectors are linearly independent or linearly dependent.

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Q: 9. Find all real values of c such that the vectors and +3 are linearly independent.

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Q: (a) Show that the vectors v1 = (0, 3, 1, – 1), v2 = (6, 0, 5, 1), and v3 = (4, – 7, 1, 3) form a…

A: We have to check  linear dependent

Q: Determine all values of the constant k for which the vectors and are linearly dependent.

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Q: })- The vectors and are Select one: a. Linearly dependent b. Linearly independent

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: Let u and v = .A vector orthogonal to both ú and v is

A: