For any 3 × 3 matrix M , let | M | denote the determinant of M . Let E= [ array ccc 1 & 2…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
For any 3 × 3 matrix M, let |M| denote the
determinant of M. Let
\[E=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & 13 & 18 \end{array}\right], P=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}\right]\]
\[\text { and } F=\left[\begin{array}{ccc} 8 & 18 & 13 \\ 2 & 4 & 3 \end{array}\right]\]
If Q is a nonsingular matrix of order 3 × 3, then which of the following statements is (are) TRUE?
determinant of M. Let
\[E=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 8 & 13 & 18 \end{array}\right], P=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}\right]\]
\[\text { and } F=\left[\begin{array}{ccc} 8 & 18 & 13 \\ 2 & 4 & 3 \end{array}\right]\]
If Q is a nonsingular matrix of order 3 × 3, then which of the following statements is (are) TRUE?
- F = PEP and
- |EQ + PFQ–1| = |EQ| + |PFQ–1|
- |(EF)3| > |EF|2
- Sum of the diagonal entries of P–1EP + F is equal to the sum of diagonal entries of E + P–1FP
Answer
(D) Sum of the diagonal entries of P –1 EP + F is equal to the sum of diagonal entries of E + P –1 FP
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