Write as a Vector Equality

Problem

{[3*(2*x+y)+5*z=−1],[2*(x−3*y+4*z)=−9],[4*(1+x)=−3*(z−3*y)])

Solution

1. Expand the terms in each equation to remove parentheses.

6*x+3*y+5*z=−1

2*x−6*y+8*z=−9

4+4*x=−3*z+9*y

2. Rearrange the third equation into standard form a*x+b*y+c*z=d by moving variables to the left and constants to the right.

4*x−9*y+3*z=−4

3. Identify the coefficients of x y and z to form the coefficient matrix A

A=([6,3,5],[2,−6,8],[4,−9,3])

4. Define the variable vector v and the constant vector b

v=([x],[y],[z])

b=([−1],[−9],[−4])

5. Construct the vector equality in the form A*v=b

([6,3,5],[2,−6,8],[4,−9,3])*([x],[y],[z])=([−1],[−9],[−4])

Final Answer

([6,3,5],[2,−6,8],[4,−9,3])*([x],[y],[z])=([−1],[−9],[−4])

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