Find the value of ๐ด 2 , where A is a 2×2 matrix whose elements are given by ๐‘Ž๐‘–๐‘— = {1 if i ≠j 0 if i = j

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Transcript

Question 5 (Choice 1) Find the value of ๐ด2 , where A is a 2 ร— 2 matrix whose elements are given by ๐‘Ž๐‘–๐‘— = {โ–ˆ(1 ๐‘–๐‘“ ๐‘– โ‰ ๐‘—@0 ๐‘–๐‘“ ๐‘–=๐‘—)โ”ค A = [โ– 8(๐‘Ž_11&๐‘Ž_12@๐‘Ž_21&๐‘Ž_22 )] A = [โ– 8(0&1@1&0)] Now, A2 = [โ– 8(0&1@1&0)] ร— [โ– 8(0&1@1&0)] = [โ– 8(0(0)+1(1)&0(1)+1(0)@1(0)+0(1)&1(1)+0(0))] = [โ– 8(๐Ÿ&๐ŸŽ@๐ŸŽ&๐Ÿ)]

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.