algebra Deteminant

Question

a) If you want to calculate the determinant D =

Row 1: 1 0 3 −1

Row 2: 5 2 0 3

Row 3: 2 1 −4 0

Row 4: −3 5 0 2

which row or column should you choose to expand along to make the calculation as simple as possible?

(b) Calculate D.

(c) Without doing any calculations, just by looking at the determinant, find a value of c that makes the determinant

Row 1: 1 −2 3

Row 2: −1 c 0

Row 3: 3 −6 −8

equal to zero.

(d) Calculate the determinant of the matrix

Row 1: 0 1 7 −13

Row 2: 2 0 −5 8

Row 3: 0 0 0 3

Row 4: 0 0 −1 0

just by looking at it.



Answer 1

a. Column 3, because it has two 0 entries.

c. Let c = 2. Then the first 2 columns are multiples of each other.

d, Switch rows 1 and 2. Switch rows 3 and 4. The resulting matrix is triangular which makes determinant calculation very easy.