Write as a Vector Equality

Problem

{[10=d],[7=a+b+c+d],[−11=27*a+9*b+3*c+d],[−14=64*a+16*b+4*c+d])

Solution

1. Identify the variables and the constants in the system of linear equations. The variables are a b c and d

2. Arrange each equation so that the variables are on one side and the constants are on the other, ensuring the variables follow the same order (a,b,c,d in every equation.

3. Extract the coefficients from the left-hand side of the equations to form a coefficient matrix.

4. Represent the system as a single vector equality in the form M*v=b where M is the matrix of coefficients, v is the column vector of variables, and b is the column vector of constants.

Final Answer

[[0,0,0,1],[1,1,1,1],[27,9,3,1],[64,16,4,1]]*[[a],[b],[c],[d]]=[[10],[7],[−11],[−14]]

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