Matrices & Linear Algebra Practice Questions (Q1-5) - Statistical Sciences

1

ICAR PG Statistical Sciences 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Let $A$ be $5 \times 5$ skew-symmetric matrix, then the determinant of $A$ is:

मान लीजिए $A$ एक $5 \times 5$ विषम-सममित आव्यूह (skew-symmetric matrix) है, तो $A$ का सारणिक (determinant) है:

0 0 1 1 -1 -1 1/2 1/2

2

ICAR PG Statistical Sciences 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Which of the following statement is true?

निम्नलिखित में से कौन सा कथन सत्य है?

Every empty set is linearly dependent प्रत्येक रिक्त समुच्चय रैखिकतः आश्रित होता है Every non empty set is linearly independent प्रत्येक अरिक्त समुच्चय रैखिकतः स्वतंत्र होता है Every non empty set is linearly dependent प्रत्येक अरिक्त समुच्चय रैखिकतः आश्रित होता है Single non-zero set is linearly independent एकल अशून्य सदिश का समुच्चय रैखिकतः स्वतंत्र होता है

3

ICAR PG Statistical Sciences 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Let $A$ be an $n \times n$ matrix of real number such that $A^2 = A$, then the Eigen values of $A$ are:

मान लीजिए $A$ वास्तविक संख्याओं का एक $n \times n$ आव्यूह है जिससे $A^2 = A$ हो, तो $A$ के आइगेन मान (Eigen values) हैं:

0, 1 0, 1 1, -1 1, -1 1, -1 1, -1 -1, -1 -1, -1

4

ICAR PG Statistical Sciences 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Let $A = \begin{bmatrix} 2 & 1 & 4 \\ 3 & 2 & 5 \\ 0 & -1 & 1 \end{bmatrix}$ be a matrix, then the rank of $A$ is:

मान लीजिए $A = \begin{bmatrix} 2 & 1 & 4 \\ 3 & 2 & 5 \\ 0 & -1 & 1 \end{bmatrix}$ एक आव्यूह है, तो $A$ की जाति (rank) है:

0 0 1 1 2 2 3 3

5

ICAR PG Statistical Sciences 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

The solution of the system of equations: $$x_1 - 3x_2 + 4x_3 = 3$$ $$2x_1 - 5x_2 + 7x_3 = 6$$ $$3x_1 - 8x_2 + 11x_3 = 11$$ is given by:

समीकरण निकाय: $$x_1 - 3x_2 + 4x_3 = 3$$ $$2x_1 - 5x_2 + 7x_3 = 6$$ $$3x_1 - 8x_2 + 11x_3 = 11$$ का हल क्या है?

$x_1 = 3, x_2 = 0, x_3 = 2$ $x_1 = 3, x_2 = 0, x_3 = 2$ $x_1 = 0, x_2 = 0, x_3 = 0$ $x_1 = 0, x_2 = 0, x_3 = 0$ $x_1 = 1, x_2 = 0, x_3 = 2$ $x_1 = 1, x_2 = 0, x_3 = 2$ No solution exists कोई हल मौजूद नहीं है

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