ashleysoto7426 ashleysoto7426
  • 15-01-2020
  • Mathematics
contestada

If D is an n × n diagonal matrix with entries dii, then det D = d11d22 ∙ ∙ ∙ dnn. Verify this theorem for 2 × 2 matrices.

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MechEngineer
MechEngineer MechEngineer
  • 15-01-2020

Answer:

Verified

Step-by-step explanation:

Let the diagonal matrix D with size 2x2 be in the form of

[tex]\left[\begin{array}{cc}a&0\\0&d\end{array}\right][/tex]

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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