Explore topic-wise MCQs in Linear Algebra.

This section includes 4 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the value of A3-3A2-28A, A = \(\begin{bmatrix}-1&2&8\\-2&3&0\\-4&5&1\end{bmatrix}\).

A. \(\begin{bmatrix}80&-126&-504\\126&-172&-63\\252&-316&-46\end{bmatrix}\)
B. \(\begin{bmatrix}80&-126&-504\\126&-172&-63\\252&-315&-46\end{bmatrix}\)
C. \(\begin{bmatrix}40&-126&-504\\126&-172&-63\\252&-315&-46\end{bmatrix}\)
D. \(\begin{bmatrix}40&-126&-504\\126&-172&-63\\252&-316&-46\end{bmatrix}\)
Answer» C. \(\begin{bmatrix}40&-126&-504\\126&-172&-63\\252&-315&-46\end{bmatrix}\)
Discussion
2.

Find the value of 2A3+4A2, where = \(\begin{bmatrix}5&0&-1\\1&2&-1\\-3&4&1\end{bmatrix}\).

A. \(\begin{bmatrix}-200&0&-24\\24&-32&-24\\-72&96&-56\end{bmatrix}\)
B. \(\begin{bmatrix}-200&0&-24\\24&-32&-12\\-72&96&-56\end{bmatrix}\)
C. \(\begin{bmatrix}-200&0&-24\\12&-32&-24\\-72&96&-56\end{bmatrix}\)
D. \(\begin{bmatrix}-100&0&-12\\12&-16&-12\\-36&48&-28\end{bmatrix}\)
Answer» D. \(\begin{bmatrix}-100&0&-12\\12&-16&-12\\-36&48&-28\end{bmatrix}\)
Discussion
3.

Find the value of A3+19A, A=\(\begin{bmatrix}2&-3&1\\2&0&-1\\1&4&5\end{bmatrix}\).

A. \(\begin{bmatrix}42&-14&70\\21&+21&-21\\105&119&203\end{bmatrix}\)
B. \(\begin{bmatrix}42&-7&70\\21&-21&-21\\105&119&203\end{bmatrix}\)
C. \(\begin{bmatrix}42&-14&70\\21&-21&-21\\105&119&203\end{bmatrix}\)
D. \(\begin{bmatrix}42&-7&70\\21&+21&-21\\105&119&203\end{bmatrix}\)
Answer» D. \(\begin{bmatrix}42&-7&70\\21&+21&-21\\105&119&203\end{bmatrix}\)
Discussion
4.

Find the inverse of the given Matrix, using Cayley Hamilton’s Theorem.A=\(\begin{bmatrix}1&2&3\\2&3&4\\3&4&5\end{bmatrix}\)

A. A-1=\(\frac{1}{16} \begin{bmatrix}2&-3&-1\\4&-2&-6\\-6&9&11\end{bmatrix}\)
B. A-1=\(\frac{1}{8} \begin{bmatrix}2&-3&-1\\4&-2&-3\\-6&9&11\end{bmatrix}\)
C. A-1=\(\frac{1}{16} \begin{bmatrix}2&-1&-1\\4&-2&-6\\-6&9&11\end{bmatrix}\)
D. A-1=\(\frac{1}{8} \begin{bmatrix}2&-3&-1\\4&-2&-6\\-6&9&11\end{bmatrix}\)
Answer» E.
Discussion