I am beginner in matrix

[placid widget]

I want to find determinant of this homework exercise

[light lodge]

@placid widget are we to understand you've made zero progress so far?

[placid widget]

I only know how to add in , minus and multiple

I only know Determinant for some part

[light lodge]

do you know how to find the determinant of a 2×2 matrix in general?

[placid widget]

Yes

[light lodge]

right, then you are able to do this problem, even though it will be kind of laborious to calculate A*A*A*B*B and A*A*B*B*B

[placid widget]

I was planned to do that , but it will lost a lot of time tbh

[light lodge]

however, if you know that the determinant is multiplicative (namely that det(XY) = det(X) * det(Y) for any two matrices X and Y of the same size), then you can cut down on the amount of work

$A^3 B^2 + 4A^2 B^3$ can be factored as $A^2(AB^2 + 4B^3)$ and further as $A^2 (A+4B) B^2$

[tropic lion]

Ann

[light lodge]

so you in fact only need to know the determinants of A, B and (A+4B)

[placid widget]

Hmmm , let me try your way

Wait, is det (A^2) == (det A)^2

[light lodge]

det(XY) = det(X) * det(Y) for any two matrices X and Y of the same size

you should be able to deduce from this that the answer is yes, det(A^2) = det(A)^2

[placid widget]

Alright this will make a lot easier then

Alright that is the correct answer , now I am stuck at 3x3 matrix

Thank you for first question btw ^^

Now I want to find det of 3x3

Thank you if you are staying with me and help me solve some questions about Matrix , I was very much not understand a lot on the subject

Actually nvm I will use sarrus method

[light lodge]

sorry, i had to disappear for a moment.

finding det(A) and det(B) and multiplying them seems like it will use about the same amount of effort as first finding AB and then calculating its det

so it does not really matter which path you take here

[civic kestrel]

is this done?

[light lodge]

what's it to you

[civic kestrel]

was gonna help

...

rude much

[light lodge]

ask OP if they want any more help lmao

[civic kestrel]

thats why i asked

[placid widget]

Alright I encounter another homework

[civic kestrel]

oh

[light lodge]

oh my

that's a big matrix

[civic kestrel]

lemme see

4 x 4

[light lodge]

hang on.

...nevermind

[civic kestrel]

thats gonna be a pain

[light lodge]

||rows 1 and 3 look pretty similar. we can use that to our advantage, i think||

[civic kestrel]

oh thought it was a skew matrix for some reason

[light lodge]

gotta do some row-operation nonsense on this one i think

[civic kestrel]

@placid widget what if we do like r3-r2 and r4-r3

so that we can get its determinant?

[placid widget]

Hmmmm. I will try

[civic kestrel]

good luck bud

[placid widget]

😦 first time learn university math and already learn like 100 pages of math in first month

[civic kestrel]

THATS UNI BABBBYYYYY

[placid widget]

I actually don't know what am I doing lol

[civic kestrel]

ok so

now

using th 00

in r3 and r4

you can get a 3 x 3 matrix

i think

from c 2 3 4

[placid widget]

I actually don't know how to do that , can you instruct me?

[civic kestrel]

wait shi its been like 2 months

so

[placid widget]

I don't understand how can you have that

[silk seal]

check out this site https://matrixcalc.org/

i think for most matrices like 4x4 it makes sense to do gauß elimination and reduce it to 3x3 or even 2x2, it can also make sense to just bring it into an upper triangle form, cause then det |...| = the product of its diagonal

[fiery stream]

instead of solving it by hard multioplications, find eigen values and eigen vectors nd then convert it into diagonal matrix and then multiply

[placid widget]

.close