Consider the linear function T below. 4 T: R* → R*, X1 x1 + V5x2 X2 X2 X3 х2 — 5хз X4 -V5x4 (a) Write down the matrix of T.

Q: Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 +…

A: Here we will find matrix of linear transformation

Q: 2.x - y-z = 0 5x - 2у +2: 3 Зх + у - 2: -8

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Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

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Q: Determine by inspection whether the given set of vectors is linearly dependent of independent. Do…

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Q: X = 4 1 -3 0 0 6 1 2 -12 10 -1 = [X₁ 5 X2 X3 X4]

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Q: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: f is represented by the matrix: A = (0 2) (7 8) Show that f is invertible and find the…

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Set up the matrix which will perform the following transformation and write down its character. (x…

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Q: (a) Determine if u̟ and u2 are linearly dependent or independent. (b) Determine if u1, u2 and uz are…

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Q: 9. Show that the following statements about two vectors (a, b), (c,d) = R² are equiv- alent. (a) ad…

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Q: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

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Q: Find Jordan form of this matrix

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Q: Given u = [1 0 1] and v = [1 1 1]T (v is column matrix), evaluate the Boolean product u ʘ v

A: Given u = [1 0 1] and v = [1 1 1]T (v is column matrix), evaluate the Boolean product u ʘ v

Q: Which of the following operators in R'are linear? 1. T(x) = (8x2, -5x, -9x) %3D 2 T(x) = (10x; - 7x2…

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