Chapter 2 – Quiz 2

1. Consider A = \begin{pmatrix}1 & 0 & 1\\ 0 & 1 & 0\\-1 & 2 & -1\end{pmatrix}. What is the determinant of A? Is A invertible?

 
 
 
 

2. True or false: any identity matrix is its own inverse.

 
 

3. Which statements about matrix inversion are true? (Multiple choice)

 
 
 
 
 
 

4. Consider A=\begin{pmatrix}2 & 0\\ 1 & -4\end{pmatrix}. Invert this matrix. What is the smallest eigenvalue of the inverse A^{-1}?

 
 
 
 

5. Consider the matrix A = \begin{pmatrix} 4 & 1\\ -1 & 3\end{pmatrix}. The matrix is…

 
 
 
 
 

6. Consider two invertible matrices A, B. How can you simplify [(A\cdot B)']^{-1}? (Hint: recall the rule for the transpose of a product given early in Chapter 2.)

 
 
 
 

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