Given that || || is a vector norm on R. To show that || ||...

 

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Given that || · || is a vector norm on R". To show that || || = mar||2||=1||Ax|| is a matrix norm for n x n matrices, prove the following properties 1. ||A + B|| < ||A|| + ||B|| 2. ||AB|| < || A|||B|| Given that || · || is a vector norm on R". To show that || || = mar||2||=1||Ax|| is a matrix norm for n x n matrices, prove the following properties 1. ||A + B|| < ||A|| + ||B|| 2. ||AB|| < || A|||B||