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Linear algebra's problem

5x1 + 6x2 - 2x3 + 7x4 +4x5 = 0, 2x1 + 3x2 - x3 + 4x4 + 2x5=0, 7x1 + 9x2 -3x3 + 5x4 + 6x5=0, 5x1 +9x2 - 3x3 + x4 + 6x5 =0

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• Akarys Turganbekuly Apr 22, 2014

Find general solution of the given system of liner equation. Write general solution in terms of fundamental set of solution. What are the dimension and basis of Null space for a given system? 5x1 + 6x2 - 2x3 + 7x4 +4x5 = 0, 2x1 + 3x2 - x3 + 4x4 + 2x5=0, 7x1 + 9x2 -3x3 + 5x4 + 6x5=0, 5x1 +9x2 - 3x3 + x4 + 6x5 =0

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Posted on Jan 02, 2017

SOURCE: algebra college

Consider the following system of 3 equations in 3 unknowns:
x + y = 2
2x + 3y + z = 4
x + 2y + 2z = 6Our goal is to transform this system into an equivalent system from which it is easy to find the solutions. We now do this step by step.

• Subtract 2*(Row1) from Row2 and place the result in the second row; subtract Row1 from Row2 and place in the third row. Leave Row1 as is.
x + y = 2
y + z = 0
y + 2z = 4
• Subtract Row2 from Row3, and place the result in row3. Leave Row1 and Row2 as they are.
x + y = 2
y + z = 0
z = 4 From the last form of the system we can deduce the following unique solution to the system:
z = 4, y = -4, and x = 2-(-4) = 6Equivalently, we say that the unique solution to this system is (x, y, z) = (6, -4, 4).

Posted on Sep 17, 2008

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Edit Casio FX - 9860G SD have complex equations??

Thhe Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

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Casio FX - 9860G SD have complex equations?? edit

The Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

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Even though this post does meet your expectations, do not let that prevent you from rating it.

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