Linear Algebra

[lime shuttle]

how do i go about this?

[modest hemlock]

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[trim scarab]

Make 2 equations

A+b = c

[void yoke]

how do you define equivalent

@lime shuttle

[lime shuttle]

if we can express the equations as linear combination of the other systems equation

should i assign an arbitrary point and solve?

[void yoke]

alright, so you have two matrices A,B with same dimension

the assumption is Ker A = Ker B

[void yoke]

and now conclude precisely this

[lime shuttle]

as they have same solutions?

[void yoke]

yes, you are solving Ax = 0

the solution space is precisely the kernel of A

[lime shuttle]

so now we are again solving for constants a and b so that we can express the equations as linear combination

ae1+be2

where e1 and e2 are the equations of the system?

[void yoke]

suppose A1 is the 1st row of A, for example

A1x = 0 is an equation in the first system

provided Ker A = Ker B, show that A1 is a linear combination of the rows of B

are you allowed to use rank-nullity?

[lime shuttle]

yes we can use it

[lime shuttle]

yes got it

thanks a lot