How many symmetric 3 × 3 matrices with entries from { − 1 , 0 , 1 } have trace 1 ?

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MathematicsMatricesSymmetric & Skew Symmetric MatricesEasy2 minQB

MathematicsEasyinteger

How many symmetric $3 \times 3$ matrices with entries from ${- 1, 0, 1}$ have trace 1 ?

Answer:

162

Solution:

The diagonal is a permutation of (1,1,-1) or (1,0,0): six choices total. The three independent off-diagonal entries have $3^{3} = 27$ choices. Thus the total is 6 times 27, which is 162.

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Symmetric & Skew Symmetric Matrices

⏱ 2mℹ️ Source: QB

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