1. Solve M⋅[1,x,y]T =[39,-3,-1]T for x and y, where M=[[1,1,6],[7,6,2],[4,3,1]].

Sure, let's solve the matrix equation step by step.

First, let's write down the matrix equation:

M * [1, x, y]T = [39, -3, -1]T

where M is a 3x3 matrix:

M = [[1, 1, 6], [7, 6, 2], [4, 3, 1]]

We can rewrite the equation as a system of linear equations:

11 + 1x + 6y = 39 71 + 6x + 2y = -3 41 + 3x + 1*y = -1

Solving this system of equations, we get:

From the first equation, we can express x in terms of y:

x = 39 - 6y - 1

Substitute x into the second equation:

7 + 6*(39 - 6y - 1) + 2y = -3 234 - 36y + 2y = -3 -34y = -237 y = 237 / 34 y = 7

Substitute y = 7 into the first equation:

x = 39 - 6*7 - 1 x = 39 - 42 - 1 x = -4

So, the solution to the system of equations is x = -4 and y = 7.