Matrices Practice Questions Ques27
Question: If $F$ is a $3 \times 3$ matrix given by $F = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$, what is $F^T$?
Options:
(A) $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$
(B) $\begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}$
(C) $\begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}$
(D) $\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}$
Show Answer
Answer: A
Explanation:
(A) Correct. The transpose of the identity matrix is the identity matrix itself.
(B) Incorrect. This is not the transpose of the given matrix.
(C) Incorrect. This is not the transpose of the given matrix.
(D) Incorrect. This is not the transpose of the given matrix.
BETA
