Write as a Vector Equality x+y+z=9 , 4x+3y-z=-6 , -x-y+2z=21

Problem

{[x+y+z=9],[4*x+3*y−z=−6],[−x−y+2*z=21])

Solution

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

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

3. Extract the coefficients of y from each equation to create the second vector: ([1],[3],[−1])

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

5. Identify the constants on the right side of the equations to form the result vector: ([9],[−6],[21])

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

Final Answer

x*([1],[4],[−1])+y*([1],[3],[−1])+z*([1],[−1],[2])=([9],[−6],[21])

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