If possible express the vector v as a linear combination of V1, V2, and V3.

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Express the vector = [4] à = vi+ as a a linear combination of ₁ = [] [1] and = [] 02 V2-

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Q: Write the vector a=i−4j as the sum of a vector parallel to b=j+k, and a vector perpendicular to b.

A: Express vector a as sum of two vectors one is parallel to vector b and one is perpendicular to b.…

Q: Let A = [a₁ a2 a3 a4], and suppose that x = (4, -7, 9, 1) is in null(A). Write a4 as a linear…

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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…

Q: 44. V 3(-4V3. –2V3)

A: Given  Vector

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Determine whether the vectors v₁ =(4,-8, 12), and v₂ = (-5, 10, 15) are linearly independent; if…

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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: Find values of h for which the vectors are linearly dependent. Justify your answer. 3 7.

A: Let v1=1-14, v2=3-57, v3=-15h

Q: Determine whether the vectors v1, v2, v3 are linearly dependent or linearly independent.

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Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

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: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

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

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