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5. Investigate the following properties of determinants for matrix 𝑇:
5.1 Show that |𝑇| = |𝑇 |
|𝑇| = 4 15
= 10 and |𝑇 | = 4 2 = 10 value of the determinant remains the
2 10 15 10
same.
5.2 Interchange row 1 and 2 of 𝑇, and show that the sign of the determinant changes but
not the numeric value.
2 10
= −10 only the sign of the determinant changes
4 15
5.3 Multiply the second column of 𝑇, with 4 and investigate whether the value of the
determinant changes 4 – fold.
4 60
= 160 − 120 = 40 = 4(10) value of the determinant changes 4 – fold.
2 40
5.4 Subtract each element of row 2 from the corresponding element of row 1, show that
the value of the determinant remains the same.
2 5
= 10 value of the determinant remains the same.
2 10
5.5 Substitute column 2 with 12 and 6, so that column 2 is a multiple of column 1. Show
that the determinant of the new matrix is zero.
4 12 = 0 the determinant of the new matrix is zero.
2 6
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