The vectors V= 5 El 6 -17 u= are linearly independent if and only if k 4 8 -5+k , and w = 2 8 -18

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: 1 4 7 Determine whether the set of vectors 2 3 6 9 is linearly dependent or not. If so, find a way…

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Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

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Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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Q: , ö2= 03 = Are the vectors ü1, ö2 and ū3 linearly independent? choose If the vectors are…

A: Given vectors, v1   = 34 , v2 = -4-1 , and v3 = -811 v1 , v2 and v3 will be linearly independent if…

Q: What if the vector v was [ 7, 11, 3]

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Q: Find a vector orthogonal to both = 10 2 and w = 2

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Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

A: Here we have to check whether the given vector b→=745 is linear combination of vectors v1→=1-2-5 and…

Q: Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly…

A: See the attachment

Q: Write each vector as a linear combination of the vectors in S. (Use s, and s2, respectively, for the…

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Find the stable vector of 7 P = 2/7 M5 iii

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

A: Solution:-

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: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

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Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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Q: D1 = (12, 3, 9) , ô2 = (12, –15, –15), öz = (-8, 16, 18). Are the vectors1.02 and i3 linearly…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 3. Determine if the vectors work. -2 are linearly independent. Show all 0 1

A: Step 1:The given vectors are: ⎣⎢⎡​1−23​⎦⎥⎤​,⎣⎢⎡​111​⎦⎥⎤​ and ⎣⎢⎡​0−11​⎦⎥⎤​ To determine whether the…

Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

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Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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Q: Express the vector x as a linear combination of the u's. --0-0-0- 0, U₂5, U3 = -50 Select one: O A.…

A: Two matrices can only be added, if the dimensions of both matrices are the same. When two matrices…

Q: 5: The vectors v = [1 2 9] and w= [2 4 18] are linearly independent vectors. O True O False

A: We will find the given two vectors are linearly independent is true or false in the following step.

Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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