Write as a Vector Equality x+y-2z=3 , 2x+3y+z=13 , 7x+9y-4z=35

Problem

{[x+y−2*z=3],[2*x+3*y+z=13],[7*x+9*y−4*z=35])

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],[2],[7])

3. Extract the coefficients of y from each equation to create the second vector: ([1],[3],[9])

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

5. Identify the constants on the right side of the equations to create the resultant vector: ([3],[13],[35])

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

Final Answer

x*([1],[2],[7])+y*([1],[3],[9])+z*([−2],[1],[−4])=([3],[13],[35])

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