Factorising determinants Quiz

1. The operation $R_2\to R_2+3R_1$ is applied to a $3\times3$ determinant. What happens to its value?

• A. It is multiplied by 3
• B. It is unchanged
• C. It increases by 3
• D. It changes sign

2. A determinant has value 5. Two of its columns are swapped. The new value is:

• A. $5$
• B. $0$
• C. $10$
• D. $-5$

3. Row 2 of a determinant $\Delta$ is $(2x,\ 4,\ 6)$. Taking out a factor 2 gives $\Delta=$

• A. $2\times$ the determinant with row 2 $(x,\ 2,\ 3)$
• B. $\frac12\times$ the determinant with row 2 $(x,\ 2,\ 3)$
• C. $8\times$ the determinant with row 2 $(x,\ 2,\ 3)$
• D. the determinant with row 2 $(x,\ 2,\ 3)$

4. Which is a factor of $\begin{vmatrix} 1 & x & x^2 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{vmatrix}$?

• A. $x+2$
• B. $x-1$
• C. $x-2$
• D. $x+3$

5. Without expanding, the value of $\begin{vmatrix} 2 & 4 & 6 \\ 1 & 2 & 3 \\ 5 & 7 & 9 \end{vmatrix}$ is:

• A. $0$
• B. $2$
• C. $-2$
• D. $36$