# Example 16 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 16 Show that 1+a1111+b1111+c = abc (1+ 1a + 1b + 1c) = abc + bc + ca + ab Taking L.H.S 1+a1111+b1111+c Taking out a, b, c, common from R1, R2, & R3 respectively = abc 1a+1 1a 1a 1b 1b+1 1b 1c 1c 1a+1 Applying R1→ R1 + R2 + R3 = abc 1+ 1a+ 1b+ 1c 1a+ 1b+1+ 1c 1a+ 1b+ 1c+1 1b 1b+1 1b 1c 1c 1c+1 = abc 𝟏+ 𝟏𝐚+ 𝟏𝐛+ 𝟏𝐜𝟏+ 𝟏𝐚+ 𝟏𝐛+ 𝟏𝐜𝟏+ 𝟏𝐚+ 𝟏𝐛+ 𝟏𝐜 1b 1b+1 1b 1c 1c 1c+1 Taking 1+ 1𝑎+ 1𝑏+ 1𝑐 common from R1 = abc 𝟏+ 𝟏𝐚+ 𝟏𝐛+ 𝟏𝐜 111 1b 1b+1 1b 1c 1c 1c+1 = abc 𝟏+ 𝟏𝐚+ 𝟏𝐛+ 𝟏𝐜 111 1b 1b+1 1b 1c 1c 1c+1 Applying C3 → C3 – C1 = abc 1+ 1a+ 1b+ 1c 10𝟏−𝟏 1b1 1b− 1b 1c0 1c+1− 1𝑐 = abc 1+ 1a+ 1b+ 1c 10𝟎 1b10 1c01 Expanding determinant along R1 = abc 1+ 1a+ 1b+ 1c 1 1001−0 1𝑏0 1𝑐1+0 1𝑏1 1𝑐0 = abc 1+ 1a+ 1b+ 1c (1(1 – 0) – 0 + 0) = abc 1+ 1a+ 1b+ 1c (1(1)) = abc 1+ 1a+ 1b+ 1c = abc 𝑎𝑏𝑐+𝑏𝑐+𝑎𝑐+𝑎𝑏𝑎𝑏𝑐 = 𝑎𝑏𝑐+𝑏𝑐+𝑎𝑐+𝑎𝑏 = R.H.S Hence Proved

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Example 16 Important You are here

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Example 34 Important

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.