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

A mixture of alcohol and water is homogeneous while that of oil and water is heterogeneous.explain
The product of 5 and cube of x increased by the difference of 6 and x3?
The product of 5 and cube of x increased by the difference of 6 and x3?
What is Prime factorization of 153
solve for x, if. 3(x-8)-5=9(x+2)+1 the answer is 7.166 but i don't know how they got it problem: 3(x-8)-5=9(x+2)+1 Answer: 7.166
x-c/2=-3c/2solve for X
What are two ways that every place on the earth can be located?
Camille placed blocks on a table in rows and columns. All the rows and columns had the same number of blocks in them and formed a square. Which could be the tot
Round 3.047 to the nearest 100th
How do geographers determine the locations of places?