2 votes 2 votes What is the value of the given determinant ? Linear Algebra linear-algebra test-series determinant + – LRU asked Nov 22, 2021 LRU 732 views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply ankitgupta.1729 commented Nov 23, 2021 reply Follow Share $\det(3(\frac{1}{4}A)^{-1}) = 3^3 \det((\frac{1}{4}A)^{-1}) = 3^3 \times \frac{1}{\det(\frac{1}{4}A)} = 3^3 \times \frac{1}{(\frac{1}{4})^3\det(A)} = 3^3 \times 4^3 \times \frac{1}{\det(A)} = 3^3 \times 4^3 \times \frac{1}{(-2)} = 27 \times 16\times -2 =-864$ 4 votes 4 votes Shivani Shukla commented Nov 29, 2021 reply Follow Share But det is always positive na? . Here it should be 864 na ? 0 votes 0 votes Vishal_kumar98 commented Nov 29, 2021 reply Follow Share Determinants are always positive. Where have you read this? 2 votes 2 votes ankit3009 commented Nov 30, 2021 reply Follow Share @ankitgupta.1729 Sir, I understood your approach towards the problem. I have one doubt that according to property : det(kA) = k^3 . |A| , where A is 3x3 matrix, which is the one you have used I believe. Sir, if det( 3 x det( 1/4 A )^(−1) ) and det(A) = -2 , then answer would be -96, right? 0 votes 0 votes anshuman66 commented Nov 30, 2021 reply Follow Share determinant can not be always positive,we have to have some notation to show shrinking and negative represents that. someone correct me if im wrong 0 votes 0 votes ankit3009 commented Nov 30, 2021 reply Follow Share Yes correct @anshuman66. 0 votes 0 votes ankitgupta.1729 commented Dec 1, 2021 reply Follow Share @ankit3009, determinant is a number associated with square matrices. Since, $3 \times \det( \frac{1}{4} A )^{−1}$ is a value, not a square matrix, so you can’t find determinant of it. 4 votes 4 votes ankit3009 commented Dec 1, 2021 reply Follow Share Understood Sir. Thank you :) 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes det(3(1/4A)-1) = det(3(1/4)-1A-1) = det(3.4A-1) = det(12 A-1) = 123 * |A-1| = 123 * 1/|A| = 123 * 1/(-2) =-864 Psy Duck answered Jul 20, 2022 Psy Duck comment Share Follow See all 0 reply Please log in or register to add a comment.