Let A = [๐‘Ž๐‘–๐‘—] be a square matrix of order 3×3 and |A|= -7. Find the value of
๐‘Ž 11 ๐ด 21 + ๐‘Ž 12 ๐ด 22 + ๐‘Ž 13 ๐ด 23  where ๐ด ๐‘–๐‘— is the cofactor of element ๐‘Ž ๐‘–j

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  1. Class 12
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Transcript

Question 6 Let A = [๐‘Ž๐‘–๐‘—] be a square matrix of order 3 ร— 3 and |A|= โˆ’7. Find the value of ๐‘Ž11 ๐ด21 + ๐‘Ž12 ๐ด22 + ๐‘Ž13 ๐ด23 where ๐ด๐‘–๐‘— is the cofactor of element ๐‘Ž๐‘–j We know that ๏ปฟIf elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero Thus, ๐‘Ž11 ๐ด21 + ๐‘Ž12 ๐ด22 + ๐‘Ž13 ๐ด23 = 0

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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.