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Found 6 free book(s)Multiplication and Inverse Matrices - MIT OpenCourseWare
ocw.mit.eduIf we subdivide A and B into blocks that match properly, we can write the product AB = C in terms of products of the blocks: A1 A2 B1 B2 C1 C2 A3 A4 B3 B4 = C3 C4. Here C1 = A1B1 + A2B3. Inverses Square matrices If A is a square matrix, the most important question you can ask about it is whether it has an inverse A−1.
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Lecture 8: Solving Ax = b: row reduced form R
ocw.mit.eduIf b does not satisfy b3 = b1 + b2 the system has no solution. If a combination of the rows of A gives the zero row, then the same combination of the entries of b must equal zero. One way to find out whether Ax = b is solvable is to use elimination on the augmented matrix. If a row of A is completely eliminated, so is the corre