Question 176026
{{{(matrix(2,2,-7,-9,4,5))X+(matrix(2,2,3,4,4,-3))=(matrix(2,2,1,9,6,-6))}}} Start with the given equation.



{{{(matrix(2,2,-7,-9,4,5))X+cross((matrix(2,2,3,4,4,-3))-(matrix(2,2,3,4,4,-3)))=(matrix(2,2,1,9,6,-6))-(matrix(2,2,3,4,4,-3))}}} Subtract {{{(matrix(2,2,3,4,4,-3))}}} from both sides.



{{{(matrix(2,2,-7,-9,4,5))X=(matrix(2,2,-2,5,2,-3))}}} Subtract (note: to subtract the matrices, simply subtract the corresponding components)



Now let's find the inverse of {{{(matrix(2,2,-7,-9,4,5))}}}


*[invoke inverse_of_2x2_matrix -7,-9,4,5]



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{{{(matrix(2,2,-7,-9,4,5))X=(matrix(2,2,-2,5,2,-3))}}} Go back to the equation



{{{(matrix(2,2,5,9,-4,-7))(matrix(2,2,-7,-9,4,5))X=(matrix(2,2,5,9,-4,-7))(matrix(2,2,-2,5,2,-3))}}} Left multiply both sides by the inverse {{{(matrix(2,2,5,9,-4,-7))}}}




{{{(matrix(2,2,1,0,0,1))X=(matrix(2,2,5,9,-4,-7))(matrix(2,2,-2,5,2,-3))}}} Multiply {{{(matrix(2,2,5,9,-4,-7))}}} and {{{(matrix(2,2,-7,-9,4,5))}}} to get {{{(matrix(2,2,1,0,0,1))}}}




{{{(matrix(2,2,1,0,0,1))X=(matrix(2,2,8,-2,-6,1))}}} Multiply {{{(matrix(2,2,5,9,-4,-7))}}} and {{{(matrix(2,2,-2,5,2,-3))}}} to get {{{(matrix(2,2,8,-2,-6,1))}}}




{{{X=(matrix(2,2,8,-2,-6,1))}}} Multiply {{{(matrix(2,2,1,0,0,1))}}} (which is I) and X to get {{{I*X=X}}}




So the answer is 



{{{X=(matrix(2,2,8,-2,-6,1))}}}