DEt A

**trythis** · December 15th 2008, 12:28 AM

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

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

**Mush** · December 15th 2008, 02:24 AM

Originally Posted by trythis

Given $B = \left( \begin{array}{cc} 2 & 1 \\ & \\ 4 & 9 \end{array}\right)$ 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 ?
$det \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) = ad-cb$

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

$ \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)$

**mr fantastic** · December 15th 2008, 02:28 AM

Originally Posted by trythis

Given $B = \left( \begin{array}{cc} 2 & 1 \\ & \\ 4 & 9 \end{array}\right)$ 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 $\det \left( \begin{array}{cc} a & b \\ & \\ c & d \end{array}\right) = ad - bc$ .

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

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