Define T R² R² by T() = T 21 X2 a) Let u = 21 -[ and 7 = U₂ that T is a linear transformation. = 3x12x2 2x2 V₁ be two vectors in R2 and let c be any scalar. Prove V2

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: y = (−3, −2, −1, 5) and 4 5 2 1 3 0 3 2 2. 1 A= 2 -1 * REQUIRED 18. Compute the resulting vector of…

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Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

A:

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: The cross product of two vectors in R³ is defined by Let 7 b₁ 「azbs - asb2 = [FB] x 102 asbr - abs…

A:

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: The cross product of two vectors in R is defined by azb3 – azb2 [b1 x b2 a1 a2 azbı – ajb3 - a3 a,b2…

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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 basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

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Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show…

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

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: The cross product of two vectors in R is defined by Ta1 [b1 azb3 - azb2 a2 b2 azbı aıb3 %3D аз b3…

A: