IITM BS Question 5 - Week 6 Practice

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IITM BS Question 5 - Week 6 Practice | Prasnya

00:00

Q5Comprehension7 Marks21 Dec 2025

Passage

Based on the above data, answer the given subquestions. Consider the vector space

M_{2 \times 2}

, the set of all

2 \times 2

matrices with real entries, with the usual addition and scalar multiplication. Let

B_1 = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} \right\}

and

B_2 = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} -1 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & -1 \\ 0 & 1 \end{bmatrix} \right\}

be two ordered bases of

M_{2 \times 2}

Choose all the correct answers.

00:00

21 Dec 2025

Mathematics 2 · Week 6

Q5.Choose all the correct answers.@passage

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00:00

Q5Comprehension7 Marks21 Dec 2025

Passage

Based on the above data, answer the given subquestions. Consider the vector space

M_{2 \times 2}

, the set of all

2 \times 2

matrices with real entries, with the usual addition and scalar multiplication. Let

B_1 = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} \right\}

and

B_2 = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} -1 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & -1 \\ 0 & 1 \end{bmatrix} \right\}

be two ordered bases of

M_{2 \times 2}

Choose all the correct answers.

00:00

21 Dec 2025

Mathematics 2 · Week 6

Q5.Choose all the correct answers.@passage

Save

Read

Check

Details