Matrices & Determinants
Counting Matrices — Sum of Squares Condition
nta_pyq_2026_jan
Grade 12
Question:
The number of $3\times2$ matrices $A$, which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $A^TA$ is 5, is
Step-by-Step Solution
Key Concept: Sum of diagonal of $A^TA=\sum_{i,j}a_{ij}^2=5$. Elements from $\{-2,-1,0,1,2\}$: squares are $0,1,4$. Need 6 entries with sum of squares $=5$.
Total matrices $=312$.
Correct Answer: 312