Podcast
Questions and Answers
If a matrix $A$ is both symmetric and skew-symmetric, then what can be inferred about $A$?
If a matrix $A$ is both symmetric and skew-symmetric, then what can be inferred about $A$?
- $A$ is a zero matrix. (correct)
- $A$ is a unitary matrix.
- $A$ is an identity matrix.
- $A$ is a diagonal matrix.
Consider two matrices $A$ and $B$ of the same dimensions. Which of the following statements is always true?
Consider two matrices $A$ and $B$ of the same dimensions. Which of the following statements is always true?
- $(AB)^T = A^T B^T$
- $(A + B)^2 = A^2 + 2AB + B^2$
- $(A + B)^T = A^T + B^T$ (correct)
- $AB = BA$
A square matrix $A$ is invertible if and only if:
A square matrix $A$ is invertible if and only if:
- The determinant of $A$ is non-zero. (correct)
- The determinant of $A$ is zero.
- The trace of $A$ is non-zero.
- The trace of $A$ is zero.
If $A$ is a $3 \times 3$ matrix with determinant 5, what is the determinant of $2A$?
If $A$ is a $3 \times 3$ matrix with determinant 5, what is the determinant of $2A$?
Given a system of linear equations represented by $Ax = b$, where $A$ is a square matrix, under what condition does the system have a unique solution?
Given a system of linear equations represented by $Ax = b$, where $A$ is a square matrix, under what condition does the system have a unique solution?
Let $A$ be a $2 \times 2$ matrix such that $A^2 = I$, where $I$ is the identity matrix. Which of the following is NOT a possible eigenvalue of $A$?
Let $A$ be a $2 \times 2$ matrix such that $A^2 = I$, where $I$ is the identity matrix. Which of the following is NOT a possible eigenvalue of $A$?
Consider a matrix $A$. If the columns of $A$ are linearly dependent, which of the following must be true?
Consider a matrix $A$. If the columns of $A$ are linearly dependent, which of the following must be true?
If $A$ and $B$ are two $n \times n$ matrices, and $A$ is invertible, what is the determinant of $A^{-1}BA$?
If $A$ and $B$ are two $n \times n$ matrices, and $A$ is invertible, what is the determinant of $A^{-1}BA$?
Given matrix $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$, what is the trace of $A$?
Given matrix $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$, what is the trace of $A$?
For what value of $k$ will the matrix $A = \begin{bmatrix} 2 & 4 \ 6 & k \end{bmatrix}$ be singular (non-invertible)?
For what value of $k$ will the matrix $A = \begin{bmatrix} 2 & 4 \ 6 & k \end{bmatrix}$ be singular (non-invertible)?
Flashcards
Square Matrix
Square Matrix
A square matrix is a matrix with an equal number of rows and columns.
Degree of a Square Matrix
Degree of a Square Matrix
The degree of a square matrix is the order of the matrix, which refers to the number of rows or columns it has.
Study Notes
- All questions are compulsory.
- The use of calculators is prohibited.
- Numbers to the left indicate total marks.
- Each multiple choice question (MCQ) should be answered as instructed.
- Choose an answer from the four options given for the following questions.
Degree
- The degree of the square matrix |1 2| is to be written. |3 4|
- The possible answers are:
- 1 (A)
- 2 (B)
- 3 (C)
- 4 (D)
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