Write as a Vector Equality 3x-10y+z=5 , -4x+9y-z=-6 , -13y+z=2

Problem

{[3*x−10*y+z=5],[−4*x+9*y−z=−6],[−13*y+z=2])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

2. Represent the system as a linear combination of constant vectors multiplied by the variables x y and z

3. Construct the vector for x using the coefficients from the first column: 3 −4 and 0

4. Construct the vector for y using the coefficients from the second column: −10 9 and −13

5. Construct the vector for z using the coefficients from the third column: 1 −1 and 1

6. Equate the sum of these scaled vectors to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[3],[−4],[0]]+y*[[−10],[9],[−13]]+z*[[1],[−1],[1]]=[[5],[−6],[2]]

Want more problems? Check here!