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CBSE Class 12-commerce Answered

Prove that determinant is negative if a,b,c are positive and unequal. |a b c b c a c a b|  
Asked by jkd345452 | 24 Oct, 2018, 09:17: PM
answered-by-expert Expert Answer
begin mathsize 16px style open vertical bar table row straight a straight b straight c row straight b straight c straight a row straight c straight a straight b end table close vertical bar
Use space following space steps space to space show space teh space required space result.
straight C subscript 1 rightwards arrow straight C subscript 1 plus straight C subscript 2 plus straight C subscript 3
Taking space straight a plus straight b plus straight c space common space from space straight C subscript 1 space you space get
straight D equals open vertical bar table row 1 straight b straight c row 1 straight c straight a row 1 straight a straight b end table close vertical bar
straight R subscript 2 rightwards arrow straight R subscript 2 space minus space straight R subscript 1 space and space straight R subscript 3 space rightwards arrow straight R subscript 3 space minus space straight R subscript 1
Expand space it space along space 1 to the power of st space column
Solve space it space further space we space get
fraction numerator negative 1 over denominator 2 end fraction open parentheses straight a plus straight b plus straight c close parentheses open square brackets open parentheses straight a minus straight b close parentheses squared plus left parenthesis straight b minus straight c right parenthesis squared plus left parenthesis straight c minus straight a right parenthesis squared close square brackets
Where space straight a plus straight b plus straight c greater than 0 space and space open parentheses straight a minus straight b close parentheses squared plus left parenthesis straight b minus straight c right parenthesis squared plus left parenthesis straight c minus straight a right parenthesis squared greater than 0
Hence comma space determinant space is space negative. end style
Answered by Sneha shidid | 25 Oct, 2018, 10:22: AM
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