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Old December 15th, 2008, 01:28 AM
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Default 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)
Last edited by mr fantastic; December 15th, 2008 at 03:28 AM. Reason: Formatted the given matrix using latex
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Old December 15th, 2008, 03:24 AM
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Originally Posted by trythis View Post
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)
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Old December 15th, 2008, 03:28 AM
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Originally Posted by trythis View Post
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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