题目

设 alpha_(1), alpha_(2), alpha_(3) 及 beta_(1), beta_(2), beta_(3) 分别为空间V的两组基，A=[alpha_(1) alpha_(2) alpha_(3)]，B=[beta_(1) beta_(2) beta_(3)]，B=AP，则A. 向量组 alpha_(1), alpha_(2), alpha_(3) 及向量组 beta_(1), beta_(2), beta_(3) 不等价B. P为由基 beta_(1), beta_(2), beta_(3) 到基 alpha_(1), alpha_(2), alpha_(3) 的过渡矩阵C. P^-1 为由基 alpha_(1), alpha_(2), alpha_(3) 到基 beta_(1), beta_(2), beta_(3) 的过渡矩阵D. P为由基 alpha_(1), alpha_(2), alpha_(3) 到基 beta_(1), beta_(2), beta_(3) 的过渡矩阵

设 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 及 $\beta_{1}, \beta_{2}, \beta_{3}$ 分别为空间V的两组基，$A=[\alpha_{1} \alpha_{2} \alpha_{3}]$，$B=[\beta_{1} \beta_{2} \beta_{3}]$，$B=AP$，则

A. 向量组 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 及向量组 $\beta_{1}, \beta_{2}, \beta_{3}$ 不等价

B. P为由基 $\beta_{1}, \beta_{2}, \beta_{3}$ 到基 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 的过渡矩阵

C. $P^{-1}$ 为由基 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 到基 $\beta_{1}, \beta_{2}, \beta_{3}$ 的过渡矩阵

D. P为由基 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 到基 $\beta_{1}, \beta_{2}, \beta_{3}$ 的过渡矩阵

题目解答

答案

D. P为由基 $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 到基 $\beta_{1}, \beta_{2}, \beta_{3}$ 的过渡矩阵