Question
Mathematics Question on Matrices and Determinants
Let 𝑀 be a 3×3 real matrix. If 𝑃=𝑀+𝑀𝑇 and 𝑄=𝑀-𝑀𝑇, then which of the following statements is/are always TRUE?
A
det(𝑃 2𝑄 3 )=0
B
trace(𝑄+𝑄 2 )=0
C
𝑋 𝑇𝑄 2𝑋=0, for all 𝑋∈ℝ3
D
𝑋 𝑇𝑃𝑋 = 2𝑋 𝑇𝑀𝑋, for all 𝑋 ∈ ℝ3
Answer
det(𝑃 2𝑄 3 )=0
Explanation
Solution
The correct options are: A and D