How to create a coefficient matrix from a system with sin and cos functions sin ⁡ ( x 1 ) + 3 x 2 + 4 x 3 = 0 3 x 1 + 5 x 2 + cos ⁡ ( x 3 ) = 0So it's clear to me, that the coefficients 3 and 4 are in first row in my coefficient matrix, but what about the sinus term? Same in the second equation with the cosinus term. Will they be in the column vector with my x's?

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How to create a coefficient matrix from a system with sin and cos functions  sin  ⁡  (      x    1    )  +  3      x    2    +  4      x    3    =  0  3      x    1    +  5      x    2    +  cos  ⁡  (      x    3    )  =  0So it&#039;s clear to me, that the coefficients 3 and 4 are in first row in my coefficient matrix, but what about the sinus term? Same in the second equation with the cosinus term. Will they be in the column vector with my x&#039;s?

Jaida Sanders · Accepted Answer

Unfortunately, it is trigonometric system, not a linear one. Hence it cannot be expressed into the   A  x  =  b form.Try to put it in this way:  sin  ⁡  (  x  1  )  =  −  (  3      x    2    +  4      x    3    )  ;    cos  ⁡  (      x    3    )  =  −  (  3      x    1    +  5      x    2    )  ;Hence:  (  3      x    2    +  4      x    3    )  ∈  [  −  1  ,  1  ]  ;    (  3      x    1    +  5      x    2    )  ∈  [  −  1  ,  1  ]  ;Try to verify the solvability of the system by verifying those conditions.

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