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Let be a linear transformation. Suppose the matrix for relative to a basis for is. Suppose is the transition matrix from another basis to. Then the matrix forwith respect to is

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MCQs on Linear Algebra.


Let<br><img src='https://www.fatskills.com/images2/GradExams/9EDFE78D-3C4D-4DE6-B431-1FF9AC8560BF.png' height='20' width='81'/> be a linear transformation. Suppose the matrix for<br><img src='https://www.fatskills.com/images2/GradExams/38409966-4AFF-447C-8374-D83A9632557A.png' height='14' width='14'/> relative to a basis<br><img src='https://www.fatskills.com/images2/GradExams/B3BF2BFA-98E2-49F4-9555-AE9295592DC0.png' height='14' width='14'/> for<br><img src='https://www.fatskills.com/images2/GradExams/46966CA9-BBE0-4719-A5E2-76FC70B11887.png' height='15' width='14'/> is<br><img src='https://www.fatskills.com/images2/GradExams/F9B99D58-8D78-4016-9A1B-CD19DD6A1FF3.png' height='14' width='20'/>. Suppose<br><img src='https://www.fatskills.com/images2/GradExams/32D9030F-B63B-4339-BB7A-1280E79ADF50.png' height='14' width='14'/> is the transition matrix from another basis<br><img src='https://www.fatskills.com/images2/GradExams/86F13ABB-DE5A-451B-8797-8560AF830ECE.png' height='15' width='14'/> to<br><img src='https://www.fatskills.com/images2/GradExams/B3BF2BFA-98E2-49F4-9555-AE9295592DC0.png' height='14' width='14'/>. Then the matrix for<br><img src='https://www.fatskills.com/images2/GradExams/38409966-4AFF-447C-8374-D83A9632557A.png' height='14' width='14'/>with respect to<br><img src='https://www.fatskills.com/images2/GradExams/86F13ABB-DE5A-451B-8797-8560AF830ECE.png' height='15' width='14'/> is<br/>





 
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