Solve Linear Algebra Questions: Matrices, Transposes, and More!

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The discussion revolves around solving a linear algebra problem involving two matrices, A and B. The user seeks assistance with specific calculations, including the products of the matrices (AB) and (BA), the transpose of matrix B, and finding the determinant of matrix A along with a related matrix W. Participants are encouraged to apply definitions and share where they encounter difficulties. The conversation emphasizes the importance of understanding matrix operations in linear algebra.
nycxfalcon
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Hi,

I am having so much trouble with this problem, if you can help with in any way possible I will truly appreciate it. This problem deals with Linear Algebra, most important matrices.

Here is the problem,

A=

1 7 2

2 9 -4

5 11 6


B=

1 8 2

3 10 4

5 -12 6

Calculate

(a) (AB)32

(b) (BA)21

(c) the transpose of B

(d) if (A -1)31 = (1/det(A))W , find det (A) and W

Any help will do. Thank you for you for your time.
 
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This sounds like a straight forward problem of applying the definitions...
 
anyone please help me i am having a lot of trouble with the topic
 
Have you tried applying the definitions? Where do you get stuck?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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