Write as a Vector Equality 4x-2y+z=3 , 4x+5z=-4

Problem

{[4*x−2*y+z=3],[4*x+5*z=−4])

Solution

1. Identify the variables and coefficients in the system of linear equations. The variables are x y and z

2. Rewrite the second equation to include the missing variable y by using a coefficient of zero, resulting in 4*x+0*y+5*z=−4

3. Construct the coefficient matrix A using the coefficients of x y and z from each equation.

4. Define the variable vector v as a column vector containing x y and z

5. Define the constant vector b using the values on the right side of the equations.

6. Express the system as the vector equality A*v=b

Final Answer

[[4,−2,1],[4,0,5]]*[[x],[y],[z]]=[[3],[−4]]

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