4. . Consider the basis B {(1,2), (3,-1)} of R. Define T: R = You may...

 

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4. . Consider the basis B₁ {(1,2), (3,-1)} of R². Define T: R² = You may assume that T is linear. {(1,0,0). (1,1,0), (1, 1, 1)} of R³ and the basis B₂ = R³ such that T((a, b)) = (a + 2b, -a, -b). a. Find the matrix M(T) for T with respect to the standard bases in the domain and codomain. b. Find the matrix M(T) for T with respect to B₂ in the domain and B₁ in the codomain. 4. . Consider the basis B₁ {(1,2), (3,-1)} of R². Define T: R² = You may assume that T is linear. {(1,0,0). (1,1,0), (1, 1, 1)} of R³ and the basis B₂ = R³ such that T((a, b)) = (a + 2b, -a, -b). a. Find the matrix M(T) for T with respect to the standard bases in the domain and codomain. b. Find the matrix M(T) for T with respect to B₂ in the domain and B₁ in the codomain.

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