# DEt A

• Dec 15th 2008, 12:28 AM
trythis
DEt A
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)
• Dec 15th 2008, 02:24 AM
Mush
Quote:

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)$
• Dec 15th 2008, 02:28 AM
mr fantastic
Quote:

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