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Chapter 11: Q. 64 (page 741)

Prove that a 3by 3determinant in which the entries in column 1equal those in column 3has the value 0.

Short Answer

Expert verified

It is proved that the determinate in which two columns has the same set of values is zero.

Step by step solution

01

Step 1. Given Information  

We are given that a matrix same values in column 1and 3.

We have to prove that the determinant of matrix with the same values in two columns is zero.

02

Step 2. Proving the statement

Let the determinant be,

A=abadedghg

Performing row operation C3鈫�C3-C1, we get

role="math" =aba-aded-dghg-g=ab0de0gh0=0

Hence proved.

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