Which of the following is a diagonal matrix?
A$\begin{bmatrix}1&2\\0&3\end{bmatrix}$
B$\begin{bmatrix}0&0\\0&0\end{bmatrix}$
C$\begin{bmatrix}4&0&0\\0&-1&0\\0&0&2\end{bmatrix}$
D$\begin{bmatrix}1&1\\1&1\end{bmatrix}$
Answer & Solution
Correct answer: C. $\begin{bmatrix}4&0&0\\0&-1&0\\0&0&2\end{bmatrix}$
In a diagonal matrix, every non-diagonal entry must be zero.
Option C satisfies this exactly.
Although the zero matrix in option B also has all off-diagonal entries zero, the chapter separately defines zero/null matrix
the clearest standard example of a diagonal matrix here is option C.
Keep practising Unit 8B: Volumes of Revolution and Cross-Sections
Browse all Unit 8B: Volumes of Revolution and Cross-Sections questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
A square garden has area 2025 m². What is its side?Two square fields have areas in the ratio 16 : 9. The ratio of their PERIMETERS is:How many digits will be in the square root of a perfect square with EXACTLY 8 digits?What is the units digit of (1234)²?Compute the square root of 12.96 (a decimal).Compute 105² without direct multiplication:What is the smallest natural number by which 1620 must be DIVIDED so that the quotient is What is the smallest natural number by which 180 must be MULTIPLIED so that the product be