# Misc 9 - Chapter 4 Class 12 Determinants

Last updated at Jan. 23, 2020 by Teachoo

Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 9 Evaluate |โ 8(๐ฅ&๐ฆ&๐ฅ+๐ฆ@๐ฆ&๐ฅ+๐ฆ&๐ฅ@๐ฅ+๐ฆ&๐ฅ&๐ฆ)| Let โ = |โ 8(๐ฅ&๐ฆ&๐ฅ+๐ฆ@๐ฆ&๐ฅ+๐ฆ&๐ฅ@๐ฅ+๐ฆ&๐ฅ&๐ฆ)| Applying R1โ R1 + R2 + R3 = |โ 8(๐ฅ+๐ฆ+๐ฅ+๐ฆ&๐ฆ+๐ฅ+๐ฆ+๐ฅ&๐ฅ+๐ฆ+๐ฅ+๐ฆ@๐ฆ&๐ฅ+๐ฆ&๐ฅ@๐ฅ+๐ฆ&๐ฅ&๐ฆ)| = |โ 8(2x+2y&2x+2y&2x+2y@y&x+y&x@x+y&x&y)| = |โ 8(๐(๐ฑ+๐ฒ)&๐(๐ฑ+๐ฒ)&๐(๐ฑ+๐ฒ)@y&x+y&x@x+y&x&y)| Taking common 2(x + y), from R1 = ๐(๐ฑ+๐ฒ) |โ 8(1&1&1@y&x+y&x@x+y&x&y)| Applying C2โ C2 โ C1 = 2(x+y) |โ 8(1&๐โ๐&1@y&x+yโ๐ฆ&x@x+y&xโxโy&y)| = 2(x+y) |โ 8(1&๐&1@y&x&x@x+y&โy&y)| Applying C3 โC3 โ C1 = 2(x+y) |โ 8(1&0&๐โ๐@y&x&xโy@x+y&โy&yโ(x+y))| = 2(x+y) |โ 8(1&0&๐@y&x&xโy@x+y&โy&โx)| Expanding determinant along R1 = 2(x+y) (1|โ 8(๐ฅ&๐ฅโ๐ฆ@โ๐ฆ&โ๐ฅ)|โ0|โ 8(๐ฆ&๐ฅโ๐ฆ@๐ฅ+๐ฆ&โ๐ฅ)|+0|โ 8(๐ฆ&๐ฅ@๐ฅ+๐ฆ&โ๐ฆ)|) = 2(x+y) (1|โ 8(๐ฅ&๐ฅโ๐ฆ@โ๐ฆ&โ๐ฅ)|โ0+0) = 2(x+y) (1( โ x2 โ ( โy) (x โ y)) ) = 2(x+y) ( โ x2 + y (x โ y)) = 2(x+y) ( โ x2 + xy โ y2) = โ 2(x+y) ( x2 + y2 โ xy) = โ 2(x3+y3) Hence , โ = โ 2(๐ฑ๐+๐ฒ๐) (Using a3 + b3 = (a + b) (a2 + b2 โ ab))

Miscellaneous

Misc 1

Misc. 2 Important Deleted for CBSE Board 2021 Exams only

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9 You are here

Misc 10

Misc 11 Important Deleted for CBSE Board 2021 Exams only

Misc 12 Important Deleted for CBSE Board 2021 Exams only

Misc. 13 Deleted for CBSE Board 2021 Exams only

Misc 14 Deleted for CBSE Board 2021 Exams only

Misc. 15 Important Deleted for CBSE Board 2021 Exams only

Misc. 16 Important

Misc 17 Important Deleted for CBSE Board 2021 Exams only

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.