Problem 7. Recall that the standard basis of R is = [e e2] where -...
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Problem 7. Recall that the standard basis of R² is ε = [e₁ e2] where - 0₁ -8 Let where and let €1 where U = [₁ ₂], -13]. U₁ = U1 U12 V = [v₁ v₂], 3. 0 Then U and V are ordered bases of R2 (you don't need to check that). Let L: R² R2 be the linear transformation such that V2 32 - [L]uu = [87] 5 A. Find the transition matrices Seu, Sev, Sue, Sve, Suv and Syu. B. Find [L]ɛɛ, the matrix of L with respect to the standard basis. C. Find [L]vy, the matrix of L with respect to the basis V. D. Let w R2 be the vector whose coordinate vector with respect to Vis [w]}v = [-3]. Find [L(w)]y, the coordinate vector of L(v) with respect to the basis V. Find [L(v)]u. E. Express the vectors L(u₁) and L(u₂) as linear combinations of the vectos u₁ and 22. Explanation: You want to write an equation L(u₁) = au₁ + Bu₂, where a and 3 are numbers you have to find. You want to leave the symbols u₁ and u₂ alone. The following equation is in the correct form, but the numbers are wrong L(u₁) = 17u₁ + 32u2. Find a similar equation for L(u₂). Hint: What is the definition of [L]uu? Problem 7. Recall that the standard basis of R² is ε = [e₁ e2] where - 0₁ -8 Let where and let €1 where U = [₁ ₂], -13]. U₁ = U1 U12 V = [v₁ v₂], 3. 0 Then U and V are ordered bases of R2 (you don't need to check that). Let L: R² R2 be the linear transformation such that V2 32 - [L]uu = [87] 5 A. Find the transition matrices Seu, Sev, Sue, Sve, Suv and Syu. B. Find [L]ɛɛ, the matrix of L with respect to the standard basis. C. Find [L]vy, the matrix of L with respect to the basis V. D. Let w R2 be the vector whose coordinate vector with respect to Vis [w]}v = [-3]. Find [L(w)]y, the coordinate vector of L(v) with respect to the basis V. Find [L(v)]u. E. Express the vectors L(u₁) and L(u₂) as linear combinations of the vectos u₁ and 22. Explanation: You want to write an equation L(u₁) = au₁ + Bu₂, where a and 3 are numbers you have to find. You want to leave the symbols u₁ and u₂ alone. The following equation is in the correct form, but the numbers are wrong L(u₁) = 17u₁ + 32u2. Find a similar equation for L(u₂). Hint: What is the definition of [L]uu?
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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