031 Review Problems

This is a list of sample problems and is meant to represent the material usually covered in Math 31. An actual test may or may not be similar.

1. True or false: If all the entries of a $7\times 7$ matrix $A$ are $7,$ then det $A$ must be $7^{7}.$

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2. True or false: If a matrix $A^{2}$ is diagonalizable, then the matrix $A$ must be diagonalizable as well.

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3. True or false: If $A$ is a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4\times 4} matrix with characteristic equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda(\lambda-1)(\lambda+1)(\lambda+e)=0,} then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is diagonalizable.

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4. True or false: If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is invertible, then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is diagonalizable.

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