4. Define the function T: R² → R as 1 T(v) = Av = |-2 4 V2 %3D -2 a. Find T(2, 4). b. Find the prcimage of (-1, 2, 2). c. Explain why the vector (1, 1, 1) has no prcimage under this trans- formation.

Q: . Consider V1 1 and v3 = V2 = .0. 0 ) as vectors in R3. Let T: R3→R3 be a linear operator such that…

A: The solution is given as

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

A:

Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: Here given A=1-2301-44-912, b=-6-15-5 Here given linear transformation as Tx=Ax

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

A:

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: Consider the vector function r(t)=⟨t,t7,t5⟩r(t)=⟨t,t7,t5⟩ Compute ⟨r′(t)=⟨  ,  ,  ⟩⟩ ⟨T(1)=⟨  ,  ,…

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Q: Find the point on the graph of z: (x2 + + 4y") at which vector n = - P =

A: Given,  (a)   z=-x2+4y2,   n=8,-80, 2  (b) f(x, y)=ex2+2y at (0, 0)

Q: Find the Wronskian of the following vector functions: 3t-1 -t+1 u (t) = -t v (t) = 3t

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Q: 1 3 20. Find the associated P-vector. A. C. D. E. None B. ON

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Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

A:

Q: Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1)…

A: We know that Pn is the vector space of all the polynomials of degree n+1 and the basis for this…

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: Suppose T(v1) = w1 + w2 + W3 and T(v2) = w2 + w3 and T(v3) = W3. Find the matrix A for Tusing these…

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Q: Which of the followings is the vector projection of u onto v where u = -2i + 4j – V5k and v = 2i –…

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Q: Sketch the vector field. y F(7,9) = ( - 55) 2' 2 -2 -2 -2 -2 -2 2. 2. 2. 2. 2.

A: The objective is to sketch the given vector field

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

A:

Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

A: Topic:- vector

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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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: Define T: R –→ R? by T *2 *1+ 8x2 Find a non-zero vector in the kernel of T.

A:

Q: In(In t), t is The natural domain of the vector-valued function 7 (t)= O (-3, 3) O (1, 3) OR O (0,…

A: We can find individual domain of each function components.

Q: 3. Use the Wronskian to determine whether the functions fi = e*,f2 sinx and f3 = x are linearly…

A: To find- Use the Wronskain to determine the functions f1 = ex, f2 = sinx and f3 = x3 are linearly…

Q: Let x1(t), x2(t), . . .  , xn (t) be vector functions whose ith components (for some fixed i )…

A: Given that x1(t), x2(t), . . ., xn(t) be vector functions whose ith components ( for some fixed i)…

Q: Q3) Let W=span{v1,V2,...,Vp}, and let x is orthogonal to each v,,for 1<j<p. Prove or give a counter…

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Q: 1. Show that the given vector functions are linearly independent (-00,00). on x; (t) =

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Q: Use the Wronskian to determine if the function vectors 7,= x? + e* and 72= e²x are linearly…

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Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: If r(t) = (1 + t)/²i+ (1- t)/2j+tk, t 0 then the binormal vector B is اخترأحد الخيارات

A:

Q: Find a vector function that satisfies the conditions r"(t) = 12ti – 31-/2j+2k, r'(1) = j, r(1) = 2i…

A: We have to find a vector function that satisfies the conditions…

Q: Find the domain of the vector function 7(t) = (, V1-t, 1 1 – t, t t +1 A. (-0, –1) U (-1,1) В. (1,…

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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: Consider the vector-valued functions æ1(t) = 5t + 6 and æ2(t) = 3e-2t 8t2 + 3t) 3e-2t

A: In this question, we have to find the wronskian and the interval for the existence of linearly…

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

A: The vector of stable probabilities, also known as steady-state probabilities, is a vector that when…

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…

A:

Q: Consider the vector-valued function 4t-8 [{m(3. In(3-t), 5,31²-8 8 R(t) 4-1² (0, -1,4), 1. Find the…

A:

Q: When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of…

A:

Q: Find the Wronskian of the following vector functions: 31 e -31 e 3t v, (t) = -3: v2 (t) = -3 e -3:…

A:

Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: The natural domain of the vector-valued function 7 (t)=(V²-9, In(In t), t) s O [-3, 3] O R O 13, 0)…

A:

Q: Given f(x, y, z) = xy z.Which of the following is the gradient vector of f %3D at the point…

A: The given function is f(x, y, z)=xy2z3 at the point (1,-1,-1). The gradient of a function f(x, y, z)…

Q: 3. Use the Wronskian to determine whether the functions f1 = e*, f2 = sinx and f3 = x³ are linearly…

A: The Wronskian approach helps to find whether the given functions are linearly dependent or not. If…

Q: Find the Wronskian of the following vector functions: 4: -21 41 4t v, (1) - 2 (1) - -4 e 21 ", (1) =…

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

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Q: 1 Find the domain of the vector function r(f) = 4ti+ %3D t-2J O (0, 4)U(4, ) O (o, 2)U(2, ) O…

A: The domain of vector function is all values of t for which its each component function is defined…

Q: 4. Determine whether the vector functions are linearly independent. Show your work. 1 4². 2t 8t 2

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Q: 1. Determine whether the vector-valued function 't² – 9 v - F(t) = t - 3 V3t – 1, t - 3 if t < 4, t…

A: We need to check continuity at t=3.

Q: S. The image of the vector i + j – 2k under a mapping (1 2 3 defined by the matrix M, where M = 0 1…

A: