Project Using the Transformation

Problem

|[a,b,c],[d,e,ƒ],[2*g,2*h,2*i]|

Solution

1. Identify the given information, which is the value of the original 3×3 determinant.

|[a,b,c],[d,e,ƒ],[g,h,i]|=5

2. Apply the property of determinants regarding row multiplication, which states that if every element of a row is multiplied by a constant k the value of the determinant is multiplied by k

|[a,b,c],[d,e,ƒ],[k*g,k*h,k*i]|=k*|[a,b,c],[d,e,ƒ],[g,h,i]|

3. Substitute the constant k=2 into the property based on the target expression.

|[a,b,c],[d,e,ƒ],[2*g,2*h,2*i]|=2*|[a,b,c],[d,e,ƒ],[g,h,i]|

4. Calculate the final value by multiplying the original determinant value by 2

2×5=10

Final Answer

|[a,b,c],[d,e,ƒ],[2*g,2*h,2*i]|=10

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