Matrices for GATE (original) (raw)

What is the transpose of a matrix A?

[Tex] A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}[/Tex]

• [Tex] A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} a & d & g \\ b & e & h \\ c & f & i \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} a & c & b \\ g & i & h \\ d & f & e \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} a & e & i \\ b & f & g \\ c & h & d \end{bmatrix}[/Tex]

What is the determinant of a matrix used in linear algebra?

• To determine if a matrix is symmetric.
• To find the inverse of a matrix.
• To assess the linear independence of vectors.
• To calculate the rank of the matrix.

Calculate the determinant of the matrix:

[Tex] M = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}[/Tex]

Find the Inverse of the Matrix :

[Tex] A = \begin{bmatrix} 5 & 4 \\ 6 & 8 \\ \end{bmatrix}[/Tex]

• [Tex] A = \begin{bmatrix} 5 & 6 \\ 4 & 8 \\ \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} 8 & 6 \\ 4 & 5 \\ \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} 0.5 & -0.25 \\ -0.375 & 0.3125 \\ \end{bmatrix}[/Tex]
• [Tex] A = \begin{bmatrix} 0.5 & -0.375 \\ -0.25 & 0.3125 \\ \end{bmatrix}[/Tex]

If B is a skew-symmetric matrix, what type of matrix is B100?

The inverse of a 2 × 2 matrix ​[Tex]\begin{bmatrix} a & b \\ c & d\\ \end{bmatrix}[/Tex] exists if:

If A and B are 2 × 2 matrices, which of the following is true?

• (A + B) (A − B) = A2 − B2
• (A − B)(A − B) = A2 +B2 − 2AB
• (A + B)(A + B) = A2 + B2 + 2AB
• (A − B)(A + B) = A2 + AB − BA − B2

Let A and B be n × n matrices where A is invertible and B is singular. Which of the following statements is always true?

Let A be a m × n matrix and B be a n × p matrix. Which of the following is always true regarding the rank of the product AB?

• Rank(AB) ≤ min⁡(Rank(A), Rank(B))
• Rank(AB) = max⁡(Rank(A), Rank(B))

If A is a diagonal matrix, which of the following is true?

• The eigenvalues of A are the entries on its diagonal.
• A is invertible if and only if all its diagonal entries are non-zero
• A is symmetric if all its diagonal entries are real.

There are 10 questions to complete.

Take a part in the ongoing discussion