Write as a Vector Equality x+2y+3z=5 , 3x-y+2z=8 , 4x-6y-4=-2

Problem

{[x+2*y+3*z=5],[3*x−y+2*z=8],[4*x−6*y−4=−2])

Solution

1. Standardize the third equation by moving the constant term to the right side.

4*x−6*y=−2+4

4*x−6*y+0*z=2

2. Identify the coefficients of the variables x y and z for each equation to form the column vectors.

Coefficients of *x:([1],[3],[4])

Coefficients of *y:([2],[−1],[−6])

Coefficients of *z:([3],[2],[0])

3. Identify the constants on the right side of the equations to form the constant vector.

Constants:([5],[8],[2])

4. Construct the vector equality by multiplying each variable by its corresponding coefficient vector and setting the sum equal to the constant vector.

x*([1],[3],[4])+y*([2],[−1],[−6])+z*([3],[2],[0])=([5],[8],[2])

Final Answer

x*([1],[3],[4])+y*([2],[−1],[−6])+z*([3],[2],[0])=([5],[8],[2])

Want more problems? Check here!