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

Problem

{[3*a−2*y+3*a=5],[2*a+4*y−z=2])

Solution

1. Combine like terms in the first equation by adding the a terms together.

3*a+3*a=6*a

2. Rewrite the system of linear equations in standard form, ensuring all variables (a y and z are represented in each equation.

{[6*a−2*y+0*z=5],[2*a+4*y−z=2])

3. Identify the coefficients for each variable to form the coefficient matrix and the constants to form the result vector.

Coefficients for *a:[[6],[2]]

Coefficients for *y:[[−2],[4]]

Coefficients for *z:[[0],[−1]]

4. Express as a vector equality by writing the linear combination of the column vectors equated to the constant vector.

a*[[6],[2]]+y*[[−2],[4]]+z*[[0],[−1]]=[[5],[2]]

Final Answer

a*[[6],[2]]+y*[[−2],[4]]+z*[[0],[−1]]=[[5],[2]]

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