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Ex 4.2, 1 Using the property of determinants and without expanding, prove that: |β–ˆ(π‘₯ π‘Ž π‘₯+π‘Ž@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| = 0 βˆ† = |β–ˆ(π‘₯ π‘Ž π‘₯+π‘Ž@𝑦 𝑏 𝑦+𝑏@𝑧 𝑐 𝑧+𝑐)| C1 β†’ C1 + C2 βˆ† = |β–ˆ(𝒙+ 𝒂 π‘Ž 𝒙+𝒂@π’š+𝒃 𝑏 π’š+𝒃@𝒛 +𝒄 𝑐 𝒛+𝒄)| C1 and C3 is same βˆ† =𝟎 By Property: if any two row or columns of a determinant are identical then value of determinant is zero

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.