10.13 Homework: determinants

$\left|\begin{array}{cc}3& 4\\ 5& 6\end{array}\right|$

• A

  Find the determinant by hand.

• B

  Find the determinant by using your calculator.

• C

  Finally, use your calculator to find the determinant of the inverse of this matrix .

What did you get? Can you make a generalization about the "determinant of an inverse matrix"?

$\left|\begin{array}{cc}1& 2\\ 3& n\end{array}\right|=2$

• A

  What is $n$ ?

• B

  Check your answer by using your calculator.

$\left|\begin{array}{ccc}2& 4& 6\\ 1& 3& n\\ 5& 7& 9\end{array}\right|=$

$\left|\begin{array}{ccc}2& 4& 6\\ 1& 3& 8\\ 5& 7& 9\end{array}\right|$

• A

  Find the determinant by hand.

• B

  Find the determinant by using the formula you found in #3.

• C

  Find the determinant by using your calculator.

A triangle has vertices at (-1,-2), (1,5), and (3,4).

• A

  Do a quick sketch of the triangle.

• B

  Set up a determinant that will find its area.

• C

  Evaluate that determinant (use your calculator) to find the area.

• D

  Can you think of any other way to find the area of this triangle?

Use your calculator to find the determinant $\left|\begin{array}{cccc}1& 3& 4& 2\\ 6& 5& 3& 8\\ 9& 5& 9& 7\\ 4& 1& 2& 0\end{array}\right|$ .

Make up a 3×3 matrix whose determinant is zero. (Do not use all zeros!) Try to find its inverse on your calculator. What happens?