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.
Related questions
If a = 2 and b = −3, value of a² − b²:If 0 < a < b and a^2 + b^2 = 50, ab = 7, what is b − a?Solve: |2x − 5| = 3.Expand (x + y)³.If a + b = 7 and ab = 12, find a² + b².If x + 1/x = 3, find x² + 1/x².If x² + y² = 25 and xy = 12, then (x + y)² =If $z=x+iy$, what is the modulus $|z|$?
![](https://qallery.app/diagrams/v2_337fce5574f0/