2. Consider the linear transformation T: P₂ (R) → M2x2 (R) defined by ao + 2a2 T(a₂x² + a₁x + ao) = 4ao ao - 3a1 12a1 2ao + 4a2] Find the matrix for T, [T]g, where B = {1, x, x²} C = {[9.61.69.89]} are bases for P2(R) and M2x2 (R) respectively. Find bases for Ker(T) and Rng(T). Is T one-to-one, onto, neither, or both?

Q: iv) Find a basis for ker(T). 1o lamsd zied v) Determine the dimension of the ker(T). vi) Find a…

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Q: (a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2,…

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Q: Show that a orthogonal 2X 2 matrix corresponds to a rotation in R2 if <det Q = 1 and reflection…

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Q: The matrices A₁ = [18], 42 = [8], [8]₁4 = [] A3 = = form a basis for the linear space V = IR²X2.…

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Q: +4 M || 3 Find the matrix M of the linear transformation T: R³ → R² given by X1 CH = −3x₁ − x₂ +…

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Q: 15. fi = 1+ 2x – 2x2, f2 = 2 + 3x – 4x2, f3 = 1+4x – x2, B = (f1, f2; f3). 1 T(fi) = 3. 2. ,T(f2) =…

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Q: If T: R² → R³ is a linear transformation such that then the standard matrix of Tis A = T([1]) T([^])…

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Q: 2. Consider the linear transformation T : P2(R) → M2×2(R) defined by За1 ao + 2a2 |4ао — 12а, 2аg +…

A: 1st we find the matrix for T by using the bases. Then find the Ker(T) and Rng(T). After that from…

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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Q: Define T: R² R³ by T ([2]) 211 - 212 - 12 21 +372 Then we can write T(z) – Az where A =

A: If T is a linear transformation from Rn to Rm such that T(x) = Ax then A is an mxn matrix.