Find the determinant of the nxn matrix A with 5's on the diagonal, l's above the diagonal, and O's below the diagonal. det (A) =

Mathematics

1 answer:

Vilka [71]3 years ago

6 0

Answer:

n times 5

Step-by-step explanation:

A matrix Anxn of this way is called an upper triangular matrix. It can be proved that the determinant of this kind of matrix is

$a_{11}+a_{22}+...+a_{nn}$

In this case, it would be 5+5+...+5 (n times) = n times 5

We are going to develop each determinant by the first column taking as pivot points the elements of the diagonal

$det\left[\begin{array}{cccc}5&a_{12}&a_{13}...&a_{1n}\\0&5&a_{23}...&a_{2n}\\...&...&...&...\\0&0&0&5\end{array}\right] =5+det\left[\begin{array}{ccc}5&a_{23}...&a_{2n}\\0&5&a_{3n}\\...&...&...\\0&0&5\end{array}\right]=5+5+...+det\left[\begin{array}{cc}5&a_{n-1,n}\\0&5\end{array}\right]=5+5+...+5+5\;(n\;times)$

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Which triangles are congruent by AAS?

netineya [11]

For two triangles to be congruent by AAS:
1- Two angles in the first triangle must be equal to two angles in the second triangle
2- A non included side in the first triangle is equal to a non included side in the second triangle

Now, let's check our options. We will find that:
For the two triangles UTV and ABC:
angle T = angle A
angle V = angle C
TU (non-included between angles T & V) = AB (non-included between angles A & C)

Therefore, we can conclude that:
Triangles ABC and UTV are congruent by AAS

8 0

3 years ago

Read 2 more answers

PLEASE HELP!!!!!!!!!!

yan [13]

$115 = l \times 2.5 \times 5.75$