Let B = {(1,1),(3,2)} and B′ = {(4,5),(2,4)} be two bases of R2. Let v be a vector with (v)B′ = (5, −6). E denotes a standard basis for R^2 (a) Based on the definition of coordinate vectors, compute v (in the standard basis) from the coordinate vector (v)B′ = (5, −6). (b) Find the transition matrix PB←B′ . (c) Use the transion matrix PB←B′ and (v)B′ = (5,−6) to find (v)B. (d) Based on the definition of coordinate vectors, compute v (in the standard basis) from the coordinate vector (v)B that you have obtained in part (c). Does it agree with your answer from part (a)? (e) Find the transition matrix PE←B′ . (f) Find the transition matrix PB←E. (g) Compute the product PB←E, PE←B′, and explain why the product equals to PB←B′ . I want anwers for part(d)(e)(f) and (g).
Let B = {(1,1),(3,2)} and B′ = {(4,5),(2,4)} be two bases of R2. Let v be a
vector with (v)B′ = (5, −6). E denotes a standard basis for R^2
(a) Based on the definition of coordinate
(b) Find the transition matrix PB←B′ .
(c) Use the transion matrix PB←B′ and (v)B′ = (5,−6) to find (v)B.
(d) Based on the definition of coordinate vectors, compute v (in the standard basis) from the coordinate vector (v)B that you have obtained in part (c). Does it agree with your answer from part (a)?
(e) Find the transition matrix PE←B′ .
(f) Find the transition matrix PB←E.
(g) Compute the product PB←E, PE←B′, and explain why the product equals to PB←B′ .
I want anwers for part(d)(e)(f) and (g).
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