If A = [a1, a2, a3] has as columns the three vectors a1, a2, and a3. What is y = Ax, where x is a vector with three components, x1, x2, x3? Is y in the column space of A?

Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: 3. Determine if the sets of vectors given are LI or LD and explain how you know. a) {(3,4),…

A: Here we apply theorems from linearalgebra.

Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Consider the following vectors: -1 -3 -2 3 -3 4 8 For each of the following vectors, determine…

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Q: To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and…

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Q: State if the following statement is true or false. The set of vectors B={u=(2,7,3); v = (1,0,7) ;w =…

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Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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

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Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: find the diJ tance betueen the vectors

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Q: Let a = (8,-6,7) and b = (-1,4, -3) be vectors. Compute the following (the answers to A, B, C are…

A: Given vectors  a = <8,-6,7> b=<-1,4,-3>

Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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Q: Let u = (3, 6, 2), v = - (6, 7, -2), w = (24, 33, h + 0). Determine the value for h so that w is in…

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Q: Consider the vectors i = (6,4), i = (-2,6), = (4, 2), and i = (-2, 3). Which of these vectors are…

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Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: Determine by inspection the linearly independent vectors !! O a. O b. O C. с. -8 12 4 -2 2 5112]…

A: To determine by inspection the linearly independent vectors.a -812-4, 2-3-1, 000b 51, 28c 4-26, 6-39…

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: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

Q: If vector u=2:1+2:/ and vector V =5./+4/, simplify each of the following, writing your final answer…

A: Given:    u = 2i + 2j    v = 5i + 4j

Q: Let A = 10-2 04-6 and b= 0 22 Denote the columns of A by a₁. a2 a3. and let W = Span (a₁. ₂. 3) -48…

A: Part (c) asked and answered.