1. ## DEt A

Given $\displaystyle B = \left( \begin{array}{cc} 2 & 1 \\ & \\ 4 & 9 \end{array}\right)$ and det(A)=3, write down each of the following;

a)det(B)
b)det(3B)
c)det(A^3)

2. Originally Posted by trythis
Given $\displaystyle B = \left( \begin{array}{cc} 2 & 1 \\ & \\ 4 & 9 \end{array}\right)$ and det(A)=3, write down each of the following;

a)det(B)
b)det(3B)
c)det(A^3)
Where are you having problems ?
$\displaystyle det \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) = ad-cb$

$\displaystyle k \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) = \left( \begin{array}{cc} ka & kb \\ & \\ kc & kd \end{array}\right)$

$\displaystyle \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right)^{3} =\left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) \times \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) \times \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right)$

3. Originally Posted by trythis
Given $\displaystyle B = \left( \begin{array}{cc} 2 & 1 \\ & \\ 4 & 9 \end{array}\right)$ and det(A)=3, write down each of the following;

a)det(B)
b)det(3B)
c)det(A^3)
a) You should know that $\displaystyle \det \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) = ad - bc$.

b) See theorem 1 here: Pauls Online Notes : Linear Algebra - Properties of Determinants

c) Consider theorem 3 here: Pauls Online Notes : Linear Algebra - Properties of Determinants