How Can You Solve Determinants for Given Matrices?

[sara_87]

Everyone is going to start to hate me know because i keep asking so many questions, but really i do look around these boards to help someone, but the questions are to hard for me or someone answers before me!

anyway my question is:

If the determinant of

a b c
d e f
g h i

is 7

then find the following determinants:

a)

a+2d b+2e c+2f
d e f
g h i

b)

a b c
g h i
d e f

c)

a b c
d e f
5g 5h 5i

My Answer:

i don't even know where to start!

any tips?

 

[Hurkyl]

Those matrices bear resemblance to the original, don't they? ...

 

[sara_87]

yeah...
i still don't know what to do...

 

[matt grime]

You have been taught rules about how determinants change under row operations. Use them.

 

[sara_87]

wait, i wrote the question wrong (as usual, matt grime) the question is:

a b c
d e f
g h 1

is equal to 7

the other parts are the same.

if the question was the same as i had previously written it would i get:
a) =7
b) = -7
c) =35

 

[radou]

Looks correct.

 

[sara_87]

unfortunatley i wrote the question worng, in the book they replaced the i with 1...do you think that is a mistake?

 

[cristo]

unfortunatley i wrote the question worng, in the book they replaced the i with 1...do you think that is a mistake?

Either way, it doesn't matter, since we don't need to know the actual value of i in order to compute the three determinants.