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.

Respuesta :

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

Answer Link

Otras preguntas

I think of a number times it by 5 then take away from 17
What is the factored form of x^3 + 125?
Your computer server recently crashed and you need to make changes to a large manual. The manual contains approximately 16,000 words. A clerk types 4,160 words
How many pounds of mixed nuts that contain 70% peanuts must Shannon add to 15 pounds of mixed peanuts that contain 20% peanuts to make a mixture with 40% peanut
What was the name of Mariah Reynolds and James Reynolds divorce lawyer?
Round 3,872.3155 to the nearest hundred
the graph of f(x) can be compressed vertically and shifted to the left to produce the graph of g(x). if f(x)=x^3 which of the following could be the equation of
I need to no everything
List three recessive genetic disorders
which best states how the price of oil per barrel changed between 1976 and 1981? The price increased slightly. The price more than doubled. The price more than