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Math Help - DEt A

  1. #1
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    DEt A

    Given B = \left( \begin{array}{cc}<br />
2 & 1  \\<br />
& \\<br />
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 02:28 AM. Reason: Formatted the given matrix using latex
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  2. #2
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    Quote Originally Posted by trythis View Post
    Given B = \left( \begin{array}{cc}<br />
2 & 1  \\<br />
& \\<br />
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<br />
\left( \begin{array}{cc}<br />
a & b  \\<br />
& \\<br />
c & d \end{array}\right) = ad-cb


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

    <br />
\left( \begin{array}{cc}<br />
a & b  \\<br />
& \\<br />
c & d \end{array}\right)^{3} =\left( \begin{array}{cc}<br />
a & b  \\<br />
& \\<br />
c & d \end{array}\right) \times \left( \begin{array}{cc}<br />
a & b  \\<br />
& \\<br />
c & d \end{array}\right) \times \left( \begin{array}{cc}<br />
a & b  \\<br />
& \\<br />
c & d \end{array}\right)
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  3. #3
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    Quote Originally Posted by trythis View Post
    Given B = \left( \begin{array}{cc}<br />
2 & 1 \\<br />
& \\<br />
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}<br />
a & b \\<br />
& \\<br />
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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