Let A= a 0 3 0 b 5 -1/3 0 c , where a,b,c are positive integers. If trA=7, then the greatest value of A is (where trA denotes the trace of matrix A…

Question

Let A= a 0 3 0 b 5 -1/3 0 c , where a,b,c are positive integers. If trA=7, then the greatest value of A is (where trA denotes the trace of matrix A i.e. the sum of principal diagonal elements of matrix A)

MARKS Content Team · Accepted Answer

Correct answer: (C) 15. trA=a+b+c=7 Ordered triplets of a,b,c are 1,1,5,1,2,4,1,3,3,2,1,4,2,2,3,2,3,2,2,4,1,3,1,3,3,2,2,3,3,1,4,1,2,4,2,1,5,1,1 A= a 0 3 0 b 5 -1/3 0 c =abc+3b/3=abc+b A is greatest for 2,3,2 and equal to 15

Let $A = [\begin{matrix} a & 0 & 3 \\ 0 & b & 5 \\ - \frac{1}{3} & 0 & c \end{matrix}],$ where $a, b, c$ are positive integers. If $t r (A) = 7$ , then the greatest value of $|A|$ is (where $t r (A)$ denotes the trace of matrix $A$ i.e. the sum of principal diagonal elements of matrix $A$ )

Solution

More Determinants Questions

Let A=a030b5-130c, where a,b,c are positive integers. If trA=7, then the greatest value of A is (where trA denotes the trace of matrix A i.e. the sum of principal diagonal elements of matrix A)

Solution

More Determinants Questions

Let $A = [\begin{matrix} a & 0 & 3 \\ 0 & b & 5 \\ - \frac{1}{3} & 0 & c \end{matrix}],$ where $a, b, c$ are positive integers. If $t r (A) = 7$ , then the greatest value of $|A|$ is (where $t r (A)$ denotes the trace of matrix $A$ i.e. the sum of principal diagonal elements of matrix $A$ )