GATE 2023 ES – Question 48

Mathematics Foundation · Linear Algebra · 2 marks · Numerical answer

$P=\begin{pmatrix}2&3\\1&4\end{pmatrix}$,$Q=\begin{pmatrix}5&4\\0&2\end{pmatrix}$ and $R=(PQ)^T$. Find det R as an integer.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 50 to 50

Explanation

Transposition does not change determinant, and determinants multiply. Thus $\det R=\det P\det Q=(2\cdot4-3\cdot1)(5\cdot2-4\cdot0)=5(10)=\mathbf{50}$. Direct multiplication is unnecessary.

More Linear Algebra questions

GATE 2022 ES Q14 – P is m×n, Q is n×l, R and S are n×n. Assess I:(PQ)T=QTPT; II:(RS)-1=S-1R-1.
GATE 2022 ES Q37 – Find eigenvalues of pmatrix0&1\\-2&3pmatrix.
GATE 2021 ES Q36 – P+Q=pmatrix3&1\\2&12pmatrix and P-Q=pmatrix-1&-7\\8&2pmatrix. Find Q.
GATE 2026 ES Q11 – Find the matrix X satisfying 2X+pmatrix1&2\\3&4pmatrix=pmatrix3&8\\7&2pmatrix.
GATE 2026 ES Q37 – Find the eigenvalues of A=pmatrix2&2&3\\2&5&6\\3&4&10pmatrix.
GATE 2026 ES Q42 – For AX=B,where A=pmatrix2&5\\5&-2pmatrix and B=pmatrix7\\3pmatrix,which statements are…

All Linear Algebra questions →