1. Let T: R³ R³ be the linear transformation given by X1 (B)-E x2 x1 + 2x2 + x3 x1 + 3x2 + 2x3 2x1 + 5x2 + 3x3 X3 (a) Find a basis for the kernel of T, then find x ‡ y in R³ such that T(x) = T(y). (b) Find a basis for the range of T, then find v € R³ such that v is not in the range of T. T

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A: Given that the matrix A=0110 is the matrix representation of the linear transformation R2→R2. Since…

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Q: Consider the linear transformation T:R² → R³ given by the following. (Enter your answers as a…

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Q: Let TR R3 be the linear transformation given by X1 x2 T I3 == x4 3x19x25x3-7x4 - 9x5 2x16x23x3…

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Q: Let T: R5 R³ be the linear transformation given by x1 x2 3x19x25x3 — 7x4 9x5 T x3 = x4 2x16x23x3 -…

A: The solution is posted below. Please go through it.Thank you Explanation:Step 1: Step 2: Step 3:…

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Q: a) Let T: R4 → R³ be a linear transformation. 2 --0--0-0--0-0 3 -1 -1 Find T 1 3 -2 -3 if T and T 1…

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Q: Define the linear transformation T : P2 → P2 according to T (p(x)) = p(2x − 5). (a) Compute the…

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Q: Let T be a linear transformation from R into R. Find T-1 T(X 1,X2,X3) = (x1 + X3, X1 – X2 + X3,…

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A: The null space of T is the collection of all polynomials p(x) in the domain of T such that T(p(x)) =…

Q: Let T : P3 → P3 be the linear transformation such that T(-2x2) = 3x2 + 3x, T(-0.5x + 3) = 3x2 + 4x –…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Let S P₂ P₂ be the linear transformation where S(x) = -12x - 30 and S(1) = 5x + 13. 0 Suppose Mg(S)…

A: Let,      B = {x + a, x + b}  Now,        S(x + a) = S(x) + aS(1)                       = -12x - 30…

Q: Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 +…

A: ⎣⎢⎡​s+2t2s+5t2s​⎦⎥⎤​,s,t∈R⎣⎢⎢⎢⎢⎢⎡​x1​x2​x1​+2x2​+3x5​x5​x5​​⎦⎥⎥⎥⎥⎥⎤​,x1​,x2​,x5​∈R Nullity + Rank…