Write as a Vector Equality

Problem

y=C+I+G+(a−M)

Solution

1. Identify the given values for each variable provided in the task.

y=51

C=10*i

G=550

a=52

M=32*I

I=25

i=30

2. Substitute the numerical values for i and I into the expressions for C and M

C=10*(30)=300

M=32*(25)=800

3. Construct the vector v containing the variables on the right side of the equation in the order they appear: C,I,G,a,M

v=[[300],[25],[550],[52],[800]]

4. Define the coefficient vector w based on the signs and operations in the equation y=1*C+1*I+1*G+1*a−1*M

w=[[1],[1],[1],[1],[−1]]

5. Express the equation as a dot product of the coefficient vector and the variable vector to show the vector equality.

y=w⋅v

Final Answer

51=[[1],[1],[1],[1],[−1]]⋅[[300],[25],[550],[52],[800]]

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