b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

A:

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

A:

Q: i) Using Gaussian Elimination method, verify that x, = 2, x2 = -1, and x3 = 3. ii) Show that b is in…

A:

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

A:

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: x = -1/n when n is odd, and an = 1/2" when n is even

A:

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

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

A:

Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

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Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

A:

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

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: Consider the set of vectors B = {(1, 0, 2), (2, 1, -1), (3, 0, 7)} (1) Is 3 linearly independent?…

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

A: