Write as a Vector Equality x-3y+2z=8 , 2x-7y-z=-9 , x+2y-z=-7

Problem

{[x−3*y+2*z=8],[2*x−7*y−z=−9],[x+2*y−z=−7])

Solution

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

2. Extract the coefficients of x from each equation to create the first vector: ([1],[2],[1])

3. Extract the coefficients of y from each equation to create the second vector: ([−3],[−7],[2])

4. Extract the coefficients of z from each equation to create the third vector: ([2],[−1],[−1])

5. Identify the constants on the right side of the equations to form the resultant vector: ([8],[−9],[−7])

6. Combine these into a linear combination where the variables x y and z scale their respective coefficient vectors.

Final Answer

x*([1],[2],[1])+y*([−3],[−7],[2])+z*([2],[−1],[−1])=([8],[−9],[−7])

Want more problems? Check here!