Find the value of u that make the set of vectors {a, b, c, d} linearly dependent. [1 2 1 1] b = [0 1 1 -1] [1 0 0 1] C = d = [-1 8 7 u]

Q: 9

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

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Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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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: Please solve this linear algebra question. Thank you

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

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Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

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Q: Express the vector t as a linear combination of the vectors u, v, and w. 1 - 2 4 t = 0 , u = 5 , v =…

A: We use the definition of the linear combination of vectors to answer the given question.

Q: Let u, v, and w be linearly independent vectors. Show that (u+v), (u-v), and (u-2v+w) vectors are…

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Q: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

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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…

Q: Determine if the vector v is a linear combination of the remaining vectors.

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Q: Find the value(s) of h for which the vectors are linearly dependent. [1 10. 3 11.-5

A: Given vectors are L.D if

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Q: Let u1,...Ūk E V be linearly dependent vectors, and k > 2. Prove that there exists j, 1 < j < k,…

A: Given- Let v1→, ……, vk→ ∈ V be linearly dependent vectors, and k ≥ 2.  To Prove- Prove that there…

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

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Q: Find a unit vector orthogonal to both u and v. u = 8i - 16j + 4k v = 16i + 32j – 12k

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Q: Find the value(s) of h for which the vectors are linearly dependent. [1 11:-5 -2 6.

A: To find the value of h for which the vectors are linearly dependent.

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Q: Find the value of c for which the vectors -2 and c-3 in R'are linearly dependent. Select one: 1 2 O…

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Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

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

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

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Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=&lt;-1,0,1&gt; v=&lt;3,2,1&gt; w=&lt;0,1,2&gt;

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A: Given: u1=4,-4u2=4,4w=0,24

Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 11.-5 8 h 6.

A: We have to observe the relation between the vectors.

Q: Consider the vectors cO 1 (2 1 2) (1 1 0) in R3. Find the value of c, for which given vectors are…

A: The given vectors,c01, 212, 110

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

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Q: Find all real values of c such that the vectors [2 and +3 are linearly independent.

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

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Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: Find the value(s) of h for which the vectors are linearly dependent. 2 3 4 - 7 h 4

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: Find the value(s) of h for which the vectors are linearly dependent. [1 [1 3 4 10. 3 11.-5 8. -3 -2…

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Q: 3. Find the vector component of u along a and the vector component of u orthogonal to a for the…

A: Given that the vector u=2, 0, 1 and the vector a=1, 2, 3. We have to find the vector component of u…