UNIT-7 OBJECTIVE-2 PROPERTIES OF DETERMINANT
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Determinants can be evaluated using some basic properties. Some
properties are - A determinant is in triangle form if all entries below,
or above, the main diagonal are zero.

because eachelement below principal diagonal is zero, then product
of the elements of the principal diagonal is the value of the determinant.

We can show this by expansion of minors.(We'll expand by first column.)

If two columns (or rows) of a determinant are interchanged, the value of
the determinant is changed in sign.

Example 2

(from objective 1)

If we interchange columns 1 and 3 then the determinant should equal -3.

we'll expand by the first column.

If we multiply every entry in one row or column of a determinant by a constant,
the result is the same as multiplying the value of the determinant by the constant.

Example 3

(from objective1)

If we multiply the second row by 2 then the determinant should equal (3)(2)=6

(we'll expand by third column)

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