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Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 1 Prove that determinant |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| is independent of ΞΈ. Let β = |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| β = x |β 8(βπ₯&1@1&π₯)| β sin ΞΈ |β 8(βsinβ‘ΞΈ&1@cosβ‘ΞΈ&π₯)| + cos ΞΈ |β 8(βsinβ‘ΞΈ&βπ₯@cosβ‘ΞΈ&1)| = x ( βx2 β 1) β sin ΞΈ ( βxsin ΞΈ β cos ΞΈ) + cos ΞΈ (βsin ΞΈ + x cos ΞΈ) = βx3 β x + x sinβ‘γ2 ΞΈγ + π¬π’π§β‘π cos ΞΈ β sin ΞΈ cos ΞΈ + x cos2 ΞΈ = βx3 β x + x sin2 ΞΈ + x cos2 ΞΈ = βx3 β x + x (sin2 ΞΈ + cos2 ΞΈ) = βx3 β x + x (1) = βx3 (As sin2 ΞΈ + cos2 ΞΈ = 1) Hence β = βx3 Which has no ΞΈ term Thus, the determinant is independent of ΞΈ Hence Proved

Miscellaneous

Misc 1
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Misc. 2 Important

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important

Misc 12 Important

Misc. 13

Misc 14

Misc. 15 Important

Misc. 16 Important

Misc 17 Important

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

Chapter 4 Class 12 Determinants

Serial order wise

About the Author

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.