Question 176018
First, we need to find the inverse of the matrix {{{(matrix(2,2,2,4,0,1))}}}



*[invoke inverse_of_2x2_matrix 2,4,0,1]



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Now let's use the inverse matrix to find the matrix X:



{{{(matrix(2,2,2,4,0,1))X=(matrix(2,3,4,0,6,3,-1,5))}}} Start with the given equation.



{{{(matrix(2,2,1/2,-2,0,1))(matrix(2,2,2,4,0,1))X=(matrix(2,2,1/2,-2,0,1))(matrix(2,3,4,0,6,3,-1,5))}}} Left multiply both sides by the inverse {{{(matrix(2,2,1/2,-2,0,1))}}}




{{{(matrix(2,2,1,0,0,1))X=(matrix(2,2,1/2,-2,0,1))(matrix(2,3,4,0,6,3,-1,5))}}} Multiply {{{(matrix(2,2,1/2,-2,0,1))}}} and {{{(matrix(2,2,2,4,0,1))}}} to get {{{(matrix(2,2,1,0,0,1))}}} (this is the identity matrix). Let me know if you need help multiplying matrices.




{{{(matrix(2,2,1,0,0,1))X=(matrix(2,3,-4,2,-7,3,-1,5))}}} Multiply {{{(matrix(2,2,1/2,-2,0,1))}}} and {{{(matrix(2,3,4,0,6,3,-1,5))}}} to get {{{(matrix(2,3,-4,2,-7,3,-1,5))}}}.




{{{X=(matrix(2,3,-4,2,-7,3,-1,5))}}} Multiply the identity matrix (which is I) by X to get {{{I*X=X}}}



So the answer is 



{{{X=(matrix(2,3,-4,2,-7,3,-1,5))}}}