題組內容
(3). Let S = {v̂₁, v̂₂, ..., v̂ₙ} be a basis for Rⁿ and A be a n × n nonsingular matrix.
(a) Please show that \( \{A\vec{v}_1, A\vec{v}_2, \dots, A\vec{v}_n\} \) is also a basis for \( R^n \). (12%)
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(3). Let S = {v̂₁, v̂₂, ..., v̂ₙ} be a basis for Rⁿ and A be a n × n nonsingular matrix.
(a) Please show that \( \{A\vec{v}_1, A\vec{v}_2, \dots, A\vec{v}_n\} \) is also a basis for \( R^n \). (12%)