Count symmetric or skew-symmetric matrices with entries from a given set
This type of question, asked 2 times: 13 Apr 2023, 28 Jan 2025. All 2 questions below, oldest first.
Try each one first, then open its answer.
Question 1
13 Apr 2023
71
The number of symmetric matrices of order 3 , with all the entries from the set {0,1,2,3,4,5,6,7,8,9}, is :
Tap an option to check your answer.
Question 2
28 Jan 2025
71
Let M denote the set of all real matrices of order 3×3 and let S={−3,−2,−1,1,2}. Let S1={A=[aij]∈M:A=AT and aij∈S,∀i,j}S2={A=[aij]∈M:A=−AT and aij∈S,∀i,j}S3={A=[aij]∈M:a11+a22+a33=0 and aij∈S,∀i,j} If n(S1∪S2∪S3)=125α, then α equals.
