14. Which of the following is a subspace of M2,3? Justify your answer. a C. C a) U = E M2.3 b = ac b) W E E M2,3 a = -2c, f = 2e + d 0 0 d. e

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

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: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: u= (2, 1, –1) v = (-4, 3a + B, 2) w = (a, 0, 26) Find the values of a and ß such that u is parallel…

A: In this question we will use basic of calculus i.e concept of vector product. We will use the…

Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

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Q: Let D4 = {1, a, a², a³, b, ab, a²b, a³b} and X = {1, a, a²,a³}. Find i. Centralizer ofX. ii. Center…

A: Step:-1 Centralizer (C):- The centralizer of a set say S of a group say G,  is a subgroup of group G…

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: 40. Given a = (3,-4) and b = (1, 2). Find the vector a + 2b a. (5,-8) b.(5,0) c.(4,-4) d. (4,0)

A: Given,

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: 3 3. Let V = 5. Find vectors b₁, 62, 63 such that is a linear combination of b₁, b₂, b3. Additional…

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Q: Engg. Maths Memory Based Q. If the vectors (1. | 1. 2), (7,3, X. (2.3. 1) In R are Linearly…

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Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: 1 5 ]v s or fractions.) W = - 3 0

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Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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Q: If we apply Newton Raphson's method to solve the equation 2a4 – 5æ3 – 5a? + 15x – 3 = 0 |…

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Q: Express the following as a linear combination of u=(2, 1, 3), v= (1, -1, 4) and w=(2, 8, 8). (5, 14,…

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