You can definitely multiply 2x2 matrices with each other. In fact you can multiply a AxB matrix with a BxC matrix, where A, B, and C are natural numbers. That is, the number of columns of the first matrix must equal the number of rows of the second matrix--we call this "inner dimensions must match."
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2x2 - 72 would be factored into (2x - 12)(x + 6) or (2x + 12)(x - 6) To double check, multiply each pair: (2x - 12)(x + 6) = 2x2 + 12x - 12x - 72 = 2x2 - 72 (2x + 12)(x - 6) = 2x2 - 12x + 12 x - 72 = 2x2 - 72
Only square matrices have inverses.
The singular form of matrices is matrix.
Which one of those matrices is more comfortable to sleep on?
Here is a simple way to see it that will help you both understand and remember. Take two equations in two unknowns. You can generalize later. Make a 2x2 matrix using the coefficients only. Now if you multiply this equation by the vector (x,Y) written as a column and placed on the right side of the matrix and you have the 2 equations you started with. Now put the constants, that is to say what each equation is equal to, on the right side of the = sign. If you invert the coefficient matrix on the left, the 2x2 one, and multiply both sides by that inverse, the equation is solved. There is another method known as Cramer's rule that can help you to solve equations using matrices. I suggest you look that one up if you are interested or ask for some more help!