Work Problem 3 ( ): Given the vectors in R3. (11 c), (-1 0 1), (-2 1 2). a) Find the value of c, for which given vectors are linearly dependent b) Express the first one as a linear combination of two others.

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: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: If possible, find a linear combination of the form w = a₁v₁ + a₂V₂ + a3V3 where v₁ = (2, -1, 4), V₂…

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Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

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Q: 1. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

A: Let the given vectors be:w=-7116, u=-112, v=21-5. To Do: We have to write the vector w=-7116 as a…

Q: Given the following vectors A = -4a +3a-2a₂ X y B=a_+5a +7a_ X y z C=-2a-4a +6а X y Evaluate |AX…

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Q: a. A: = a: b: -1 1 1 0 A A This is the result of the inverses of the matrices: 3/2- -1/4 -3/2 5/4 0…

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Q: Q2. ()- Work out a - 2b as a column vector.

A: Given

Q: Let W= W= , V1 = , V2 = V3 = If possible, express w as a linear combination of the vectors v₁1, V2…

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Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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

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Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: 1. Let x = i +4j + 2k and y = i - 3j - k. In this question, write all vectors in i, j, k notation.…

A: Let (a) To find .(b) To find .(c) To find .(d) To find .

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: a, b, and c are vectors. Then the expression axc+bxa is (a) Meaningless (b) A vector collinear with…

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Q: Given the following vectors A=-4a +3a-2a B=a + 5a +7a X y 2 X C=-2a-4a +6a y Evaluate AX (BXC)

A: A→=-4ax+3ay-2az B→=ax+5ay+7az C→=-2ax-4ay+6az To evaluate: A→×B→×C→

Q: a. Write the vector (-4,-8,6) as a linear combination of a₁ = (1,−3,−2), ẩ₂ = (-5, -2,5) and a3 =…

A: The given vectors  and .(a) The aim is to write the vector  as a linear combination of the given…