Question

Help wanted: attachment bellow

Answer 1

@SolomonZelman

Answer 2

its a linear algebra calculus problem

Answer 3

@IrishBoy123

Answer 4

@mathmale can u help out?

Answer 5

@satellite73

Answer 6

@jim_thompson5910

Answer 7

@ganeshie8 you are my last hope..

Answer 8

As a start, can you find the derivative of each of the functions in the given basis ?

Answer 9

{0,1,cosx,-sinx}

Answer 10

right, express each of that derivative as a linear transformation of the functions in basis

Answer 11

\[a*1 + b*x + c*\sin x+d*\cos x\]

Answer 12

\(0=a*1 + b*x + c*\sin x+d*\cos x\)

\(1=a*1 + b*x + c*\sin x+d*\cos x\)

\(\cos x=a*1 + b*x + c*\sin x+d*\cos x\)

\(-\sin x=a*1 + b*x + c*\sin x+d*\cos x\)

Answer 13

find the values of a,b,c,d for each of the derivatives

Answer 14

it should be easy, can you try

Answer 15

does it req reduiced row achelon? or i'm i thinking too deep

Answer 16

Easy

Answer 17

a=b=c=0?

Answer 18

\(0=a*1 + b*x + c*\sin x+d*\cos x\)


a = b = c = d = 0 satisfies above equation yes ?

Answer 19

what about the next one :
\(1=a*1 + b*x + c*\sin x+d*\cos x\)

Answer 20

a=1, the rest 0

Answer 21

Yes. find the remaining two also similarly

Answer 22

d=1 the rest 0
c=-1 the rest 0

Answer 23

\(0=0*1 + 0*x + 0*\sin x+0*\cos x\)

\(1=1*1 + 0*x + 0*\sin x+d*\cos x\)

\(\cos x=0*1 + 0*x + 0*\sin x+1*\cos x\)

\(-\sin x=0*1 + 0*x + -1*\sin x+0*\cos x\)

Answer 24

the linear transformation matrix is formed by those values of a, b, c, d

Answer 25

those rows go as columns in the transformation matrix

Answer 26

Here it is :

\[D_x = \begin{bmatrix} 0&0&0&0\\0&1&0&0\\0&0&0&-1\\0&0&1&0\end{bmatrix}\]

Answer 27

yeh got that

Answer 28

they want you find kernel and range of \(D_x\)

Answer 29

now for range its just the transpose of the dx matrix right