If D is an n × n diagonal matrix with entries dii, then det D = d11d22 ∙ ∙ ∙ dnn. Verify this theorem for 2 × 2 matrices.
1 answer:
Answer:
Verified
Step-by-step explanation:
Let the diagonal matrix D with size 2x2 be in the form of
![\left[\begin{array}{cc}a&0\\0&d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%260%5C%5C0%26d%5Cend%7Barray%7D%5Cright%5D)
Then the determinant of matrix D would be
det(D) = a*d - 0*0 = ad
This is the product of the matrix's diagonal numbers
So the theorem is true for 2x2 matrices
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