Let I= ( array ll 1 & 0 0 & 1 array ) and P= ( array ll 2 & 0 0 & 3 array ) . Let Q= (…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let \(I=\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right) \text { and } P=\left(\begin{array}{ll}
2 & 0 \\
0 & 3
\end{array}\right) . \text { Let } Q=\left(\begin{array}{ll}
x & y \\
z & 4
\end{array}\right)\)
for some non-zero real numbers x, y, and z, for which there is a 2 × 2 matrix R with all entries being non-zero real numbers, such that QR = RP . Then which of the following statements is (are) TRUE?
for some non-zero real numbers x, y, and z, for which there is a 2 × 2 matrix R with all entries being non-zero real numbers, such that QR = RP . Then which of the following statements is (are) TRUE?
- The determinant of Q – 2I is zero
- The determinant of Q – 6I is 12
- The determinant of Q − 3I is 15
- yz = 2
Answer
(A) The determinant of Q – 2 I is zero
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