Write as a Vector Equality x+4y-7z=7 , x+y+9z=-29 , x+y+3z=11

Problem

{[x+4*y−7*z=7],[x+y+9*z=−29],[x+y+3*z=11])

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],[1],[1])

3. Extract the coefficients of y from each equation to create the second vector: ([4],[1],[1])

4. Extract the coefficients of z from each equation to create the third vector: ([−7],[9],[3])

5. Identify the constants on the right side of the equations to form the result vector: ([7],[−29],[11])

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

Final Answer

x*([1],[1],[1])+y*([4],[1],[1])+z*([−7],[9],[3])=([7],[−29],[11])

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