Let TR4 R³ be given by T(v) = Av, where 1 1 1 2 (334 1 1 1 3 0004 A = Find a basis {u₁, u₂} of ker T, and extend it to a basis {V₁, V2, U₁1, U₂} of R4. Compute w₁ = T(v₁) and w₂ = T(v₂). Find a basis {W₁, W2,Z₁} of R³. Find the matrix B of T with respect to the basis {V₁, V2, U₁, U₂} of R4 and the basis {w₁, W2, Z1} of R3. Verify that B is in canonical form.

Let TR4 R³ be given by T(v) = Av, where 1 1 1 2 (334 1 1 1 3 0004 A = Find a basis {u₁, u₂} of ker T, and extend it to a basis {V₁, V2, U₁1, U₂} of R4. Compute w₁ = T(v₁) and w₂ = T(v₂). Find a basis {W₁, W2,Z₁} of R³. Find the matrix B of T with respect to the basis {V₁, V2, U₁, U₂} of R4 and the basis {w₁, W2, Z1} of R3. Verify that B is in canonical form.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 32E

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