Write as a Vector Equality 4x+3y=0 , 3x+y+3z=0 , y+z=0

Problem

{[4*x+3*y=0],[3*x+y+3*z=0],[y+z=0])

Solution

1. Identify the variables in the system of linear equations, which are x y and z

2. Rewrite each equation to include all variables by using zero coefficients for missing terms.

4*x+3*y+0*z=0

3*x+1*y+3*z=0

0*x+1*y+1*z=0

3. Separate the coefficients into a matrix and the variables into a column vector.

([4,3,0],[3,1,3],[0,1,1])*([x],[y],[z])=([0],[0],[0])

4. Express the system as a linear combination of constant vectors scaled by the variables.

x*([4],[3],[0])+y*([3],[1],[1])+z*([0],[3],[1])=([0],[0],[0])

Final Answer

x*([4],[3],[0])+y*([3],[1],[1])+z*([0],[3],[1])=([0],[0],[0])

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