Example 3: For the given two vectors v< -2,0,1 > and w< 3, 5, -4 > find v+w, v-w, 3v, w-2v? 38 20.1 35-4) V+w= <1.5.-3> V-w= <-5.-5,5> 3v=3 <-2,0, 1>=<-6,0,3> W-2v= <3, 5, -4>-<-4, 0, 2>=<7,5,-6> (H.W sketch v+w, v-w, w-2v) V< w

Q: Set û= and w= Write as a linear combination of these two vectors For the toolbar, press ALT+F10 (PC)…

A: HHere C1 nad C2 are scalars

Q: Given the vectors v=[-1. 2, 4] and w=[0. -3, 1], which vector is perpendicular to both v and w? A…

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Q: Given the vectorsA = (2,−4) and B = (−3, 6) in R². How many pairs of real numbers r and s satisfy…

A: System of linear equations

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: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: skip the first 3 thank you

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Q: If vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1) what Is C? Explain.

A: According to question,Given vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1)

Q: is the sum of 2 vectors with components and . What is a?

A: To find the value of a, you can use the properties of vector addition.Given that the sum of the…

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: Let A = (4, –4,4, 0) and B = (-4,3, –4, 1) be points in R*

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: Given the vectors a = (4,-2) and b = (-1,9), which statements is/are true? %3D V12 82 III. 3a - b -…

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Q: Draw the vector (1,-5) in standard position. 001 8+ 7+ 6- 5 4+ 34 2 1 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2…

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Q: What vector v is given by the coordinate vector B = -21 - -5 1 1 -2 -5] -5 4 {JEJEJEJ} -5 3 -1 3 ? 5…

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

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Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: 13. Determine the dot product of the two vectors shown in the diagram. 4 -3 -2 4- 3- 1 ++ I 2 3 4…

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Q: 98. Determine whether the vectors AB and PQ are B(-2, 2, 0), where A(1, 4, 1), equivalent, P(2, 5,…

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Q: Show that the vectors (1,0,1); (-1,2,3) and (0, 1; -1) spans R³

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Q: Let u = 6 - 1 and v= 6 Show that a a -[:] k Let b = k How can it be shown that a vector b is in Span…

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Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

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 -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 u = (-1,-6,0), v= (6, 1, -3), w = (16,-9, h - 3). Determine the value for h so that w is in the…

A: To find the given questions related to span of a set :-

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.

Q: Given vectors ā = (-1,-2),5 = 2,–1), find 4a-35. (10,5) (-10,-5) (-10,5) (10,-5)

A: