2. Let A E M3(F), and suppose there are nonzero vectors u, v, w E F³ so that Au = 0, Av = -w. Show that u, v, w are linearly = v, and Aw independent.

Q: Given that {ū, 7, w} is a set of three vectors in R" determine if the set of vectors {u + w, ở – 3w,…

A: A set of vectors {v1 , v2 , v3 , . . . . vn} is linearly independent iff        a1v1 + a2v2 + . . .…

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Suppose T E L(V, W) and v1, ..., Vm is a list of vectors in V such that Tv1,..., Tvm is a linearly…

A:

Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

A:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: c for which the following vectors vi = %3D 1 P4 = are linearly independent. 1

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Q: Let y = 2-| = H and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

A:

Q: For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?

A: t+3  &amp;  2t+c2+2 Now since these vectors must be linearly independent, therefore…

Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: show that the given vector functions are linearly independent on (−∞,∞).

A: To show that the given vector functions are linearly independent x1t=   et-et,        x2t=etet

Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Determine whether the following vectors are linearly independent in R2:

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Q: Let u1,...Ūk E V be linearly dependent vectors, and k > 2. Prove that there exists j, 1 < j < k,…

A: Given- Let v1→, ……, vk→ ∈ V be linearly dependent vectors, and k ≥ 2.  To Prove- Prove that there…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: Suppose u, v, w are linearly independent vectors. Prove that S is linearly independent where (a) S=…

A: A set of vectors v1 , v2 , v3 ,...,vk from a vector space V  is said to be linearly independent , if…

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c

A: Find the slope of the given vector v=ai+ bj is given by ba.

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=&lt;-1,0,1&gt; v=&lt;3,2,1&gt; w=&lt;0,1,2&gt;

Q: for any R value of the third, so that the following vectors are linearly related and loudspeaker…

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Q: If u = x²+2x-y and v = - 2xy - 2y, then the vorticity vector is - 3yk 10 -yk 1O IIO yk IIO

A: Given u=x2+2x-yand v=-2xy-2y

Q: If v is a vector in R", and if k is any scalar, then: (a) ||v|| 20 (h) x = 0 if and only if y = 0

A: Given: v is a vector in ℝn and k is any scalar To show that  a) v≥0 b) v=0 if and only if v=0

Q: The vector v, is in Span{ v2,., Um } if and only if ( v1,., Vm ) are linearly dependent. O True O…

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Q: 2. Let i= and (a) Compute the length of the vector u.

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Consider the vectors cO 1 (2 1 2) (1 1 0) in R3. Find the value of c, for which given vectors are…

A: The given vectors,c01, 212, 110

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

A:

Q: Which of the following vectors are not linearly independent? 日L O B O A

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Q: Consider the sets of vectors  S={u,v,w} and T={u,v,w,x}. Which of the following is true:  -If T is…

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Q: If in R a vector u is orthogonal to vectors v and w, then { u, v, w} is an orthogonal set. True…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &amp;  x·w=0

Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: Consider the two vectors A = Axî + Ayĵ and B = Bxî + Byĵ. If î · î = ĵ • ĵ = 1 and î · j = ĵ · î =…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: The vector v, is in Span{ v2,., Vm } if and only if ( V Vm ) are linearly dependent. O True O False

A: Check is it dependent or not

Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: Let u and v = .A vector orthogonal to both ú and v is

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Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.