A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C 3. m(nA) = (mn)A = n(mA) 4. (m+n)A = mA + NA 5. m(A + B) = mA + mB Commutative law for addition Associative law for addition Associative law for multiplication Distributive law Distributive law

Q: Use the accompanying figure to write each vector listed as a linear combination of u and v Vectors…

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Q: Find a + b, 6a + 9b, lal, and la - bl. (Simplify your vectors completely.) a = (-6, 8), b = (6, -1)…

A: a=-6,8 ,b=6,-1

Q: Because [-37-2]] + [-27-5j]= and The [-21-5j] + [-3i-2j] = we can conclude that vector addition is +…

A: The solution is mentioned below.

Q: Determine a so that the vector u= "- [3] is a linear combination u = av+bw of vectors *-[2]· *-6). =…

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Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

Q: (d) s(v+ww) × (rv)

A: Given that u→,v→,w→∈ℝ3 and r ,s ∈ℝ.

Q: 4. Subtract the vectors shown. (blue - green)

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Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Current Attempt in Progress Find the scalar triple product u · (v x w). u-(-8,4,4), v- (5,1, - 4), w…

A: Given: u=-8,4,4, v=5,1,-4, w=-7,4,3 To find: u·(v×w)

Q: Calculate v x w = (u1,u2, u3). v = (9,5, 4) w = (-4, 8, –5) (Give your answer using component form…

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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: What is the component form of v?

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Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

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Q: 4. Three vectors are so related that A +C = 5 + j15 and A + 2B = 0. Where B is the conjugate of C,…

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Q: v•u -2 Compute u· u, v•u, and using the vectors u = and v = 4 7 n.n u•u= - 20 (Simplify your…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: V•U Compute u. u, v. u, and using the vectors u = u u u U= (Simplify your answer.) -5 ... and v= 6 3

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Q: ving decide if the statement is true or false. Remember a mathematical statement is true only if it…

A: True   The detailed solution is as follows below:

Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 0, -4). Find 2u + 3v - w. STEP 1: Multiply each…

A: Given that the vectors u=1,2,3v=2,2,-1w=4,0,-4    .

Q: If v and w are two vectors in standard position (that is with the tail at the origin) in R", then…

A: The given statement is: If v→ and w→ are two vectors in standard position ( that is with the tail at…

Q: ste each vector as a linear combination of the vectors in S. (Use 51 and 52, respectively, for the…

A: Note : " As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: Determine the dot product of the two vectors shown in the diagram. (3.5) 1. -5 4 -2 -11 23 4 5 -2+…

A: Dot product of the given vectors

Q: 2. Let r ER and (1), (†), R is the set {u, v, w} linearly independent? a) For which values r b) For…

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Q: Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by: (vi, v2) O (W1, w2) :=…

A: The objective of the question is computing the values.

Q: 1. Let x = i +4j + 2k and y = i - 3j - k. In this question, write all vectors in i, j, k notation.…

A: Let (a) To find .(b) To find .(c) To find .(d) To find .

Q: The magnitude and vector operations.  If v = (5, 3, 1)    and    u= (3, 2, 4)  what is 2|| 2v -…

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Q: Are the vectors -2-x², 1+ 2x + x² and 2x - 2-2 linearly independent? choose If the vectors are…

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