Find the Variables

Problem

[[x2,3],[1,3*x]]*[[3,6],[2,x]]=[[1,0],[0,1]]

Solution

1. Perform matrix multiplication on the left side by multiplying rows of the first matrix by columns of the second matrix.

[[(x2)*(3)+(3)*(2),(x2)*(6)+(3)*(x)],[(1)*(3)+(3*x)*(2),(1)*(6)+(3*x)*(x)]]=[[1,0],[0,1]]

2. Simplify the entries of the resulting matrix.

[[3*x2+6,6*x2+3*x],[3+6*x,6+3*x2]]=[[1,0],[0,1]]

3. Set corresponding entries equal to create a system of equations.

3*x2+6=1

6*x2+3*x=0

3+6*x=0

6+3*x2=1

4. Solve the linear equation 3 + 6x = 0ƒ*o*r$.

6*x=−3

x=−1/2

5. Verify the solution by substituting x=−1/2 into the other equations.

3*(−1/2)2+6=3*(1/4)+6=3/4+6=27/4

6. Identify the contradiction as the entry 3*x2+6 must equal 1 but 27/4≠1 Since no value of x satisfies all four equations simultaneously, there is no solution.

Final Answer

No solution

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