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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. 2 Important Not in Syllabus - CBSE Exams 2021
Misc 3
Misc 4
Misc 5
Misc 6 Important
Misc 7 Important
Misc 8
Misc 9
Misc 10
Misc 11 Important Not in Syllabus - CBSE Exams 2021
Misc 12 Important Not in Syllabus - CBSE Exams 2021
Misc. 13 Not in Syllabus - CBSE Exams 2021
Misc 14 Not in Syllabus - CBSE Exams 2021
Misc. 15 Important Not in Syllabus - CBSE Exams 2021
Misc. 16 Important
Misc 17 Important Not in Syllabus - CBSE Exams 2021
Misc 18
Misc 19 Important
Matrices and Determinants - Formula Sheet and Summary
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