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Chapter 3: Q9P (page 95)

Show without computations that the following determinant is equal to zero. Hint: Consider the effect of interchanging rows and columns.

|02-3-2043-40|

Short Answer

Expert verified

It has been proved that the determinant is zero.

Step by step solution

01

Results used

Facts used about determinants:

  1. If each element of one row of a determinant is multiplied by a number k, the determinant becomes k times.
  2. The value of a determinant remains the same if rows are written as columns and columns as rows.
02

Show that the determinant is zero

Consider,D=02-3-2043-40

Write each row as a column and vice versa, using fact 2 as:

D=0-2320-4-340

Multiply each row by -1. So Using fact 1, the determinant is

D=-1302-3-20-43-40=-D

Thus,

D+D=02D=0D=0

Hence, determinant is zero.

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