Which of the following statement(s) is/are correct?
(i) Every skew-symmetric matrix is non-inver... VIDEO
Which of the following statement(s) is/are correct?
(i) Every skew-symmetric matrix is non-invertible.
(ii) If \( \mathrm{A} \) and \( \mathrm{B} \) are two \( 3 \times 3 \) matrices such that \( \mathrm{AB}=\mathrm{O} \), then alteast one of \( \mathrm{A} \) and \( \mathrm{B} \) must be null matrix.
(iii) If the minimum number of cyphers in an upper triangular matrix of order \( n \) is 5050 , then the order of matrix is 101.
(iv) If \( A \) and \( B \) are two square matrices of order 3 such that det. \( \mathrm{A}=5 \) and det. \( \mathrm{B}=2 \), then det. (10AB) equals \( 10^{4} \)
(a) (i), (ii), (iii)
(b) (ii), (iii), (iv)
(c) (i), (ii), (iii), (iv)
(d) (iii), (iv)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-08 Let the matrix \( A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right... 2023-06-08 If the matrix \( M_{r} \) is given by \( M_{r}=\left[\begin{array}{cc}r & r-1 \\ r-1 & r\end{arr... 2023-06-08 A determinant of second order is made with the elements 0 and 1 . The number of determinants wit... 2023-06-08 Let \( \mathrm{S}=\{\sqrt{n}: 1 \leq n \leq 50 \) and \( n \) is odd \( \} \)
Let \( \mathrm{a} ... 2023-06-08 If \( \mathrm{A} \) is an invertible matrix of order 3 and \( \mathrm{B} \) is another matrix of... 2023-06-08 Let \( A, B, C \) be three square matrices such that \( A B C+A B+ \) \( B C+A C+A+B+C=O \). If ... 2023-06-08 If \( A=\left[\begin{array}{cc}-1 & 1 \\ 0 & -2\end{array}\right] \), then \( \left|A^{2}+3 A+2 ... 2023-06-08 Given \( A=\left[\begin{array}{lll}1 & 1 & 1 \\ 2 & 4 & 1 \\ 2 & 3 & 1\end{array}\right], B=\lef... 2023-06-08 Let \( I_{n} \) is a \( (n \times n) \) identity matrix and \( O_{n} \) is a \( (n \times n) \) ... 2023-06-08 If \( A \) and \( B \) are square matrices of order 3 such that \( |A|=3 \) and \( |B|=2 \), the... 2023-06-08 Which of the following statement(s) is/are correct?
(i) Every skew-symmetric matrix is non-inver... 2023-06-08 If \( \mathrm{A}_{1}, \mathrm{~A}_{3}, \ldots \ldots \ldots \mathrm{A}_{2 n-1} \) are \( \mathrm... 2023-06-08 If \( A=\left[\begin{array}{ccc}1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1\end{array}\right] \), then... 2023-06-08 If \( \mathrm{A}=\operatorname{diag}(2,-1,3), \mathrm{B}=\operatorname{diag}(-1,3,2) \), then \(... 2023-06-08 \( \left[\begin{array}{lll}7 & 1 & 2 \\ 9 & 2 & 1\end{array}\right]\left[\begin{array}{l}3 \\ 4 ... 2023-06-08 If \( A=\left[\begin{array}{ccc}0 & 1 & -2 \\ -1 & 0 & 5 \\ 2 & -5 & 0\end{array}\right] \), the... 2023-06-08 Let \( \mathrm{A}=\left[\begin{array}{c}3 x^{2} \\ 1 \\ 6 x\end{array}\right], \mathrm{B}=[a b c... 2023-06-08 If \( \mathrm{A} \) and \( \mathrm{B} \) are \( 3 \times 3 \) matrices such that \( \mathrm{AB}=... 2023-06-08 Let \( (x, y) \) be such that
\[
\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2}
\... 2023-06-08 If \( A=\left[\begin{array}{cc}4 & 2 \\ -1 & 1\end{array}\right] \) and \( I \) is the identity ... 2023-06-08 Number of integral values of \( K \) for which the system of equations;
\[
\begin{array}{l}
\cos...