Multiplication of matrix How to calculate the matrix A = 24 b = - 24 AB = 0 0 -3 -6 1 -2 0 0
2×(-2)+4×1=0
2×4+4×(-2)=0
-3×(-2)+(-6)×1=0
-3×4+(-6)×(-2)=0
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- 1. Another problem is, what conditions should be satisfied for multiplication of two matrices
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- 3. A is a matrix of order 3, a * is the adjoint matrix of a, | a | = 1, find | (2a) ^ - 1 + 3a*|
- 4. Let a be a matrix of order n, satisfy 2A ^ 2-3a + 5I = 0, and prove (a-3i) = - 1 / 14 (2a + 3I) speed
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- 9. If a and B of the same type have the same rank, then R (a) = R (b) = R (a,
- 10. Let a be a real matrix of order n and a ^ t be a transpose matrix of order A. It is proved that R (a) = R (a ^ TA) Even give 100 points for the answer
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- 13. Is the last line of the row ladder matrix all zero? It's written in the book, but I don't know what's going on. Is it a convention? It's not stated in the definition,
- 14. Is this the simplest form of row ladder matrix? A=0 -2 1 0 0 0 3 0 -2 0 0 0 -2 3 0 0 0 0 It can be reduced to 0 - 21 100 0 0 0 0 -1 0 0 0 0 0 0 1 Can continue to be transformed into 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 or 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 According to the definition of row ladder minimalist matrix: all the elements under the ladder are 0, and the number of steps is the number of non-zero rows. The first element behind the vertical line of the ladder is non-zero, which is also the first non-zero element of the non-zero row, and all other elements in its column are 0. * * * the row minimalist matrix of a matrix is uniquely determined*** All the above matrices meet the above definition, but the asterisk says that the only way to be sure is to have only one. Why? Is it not the simplest form if it can be simplified again? But the simplest answer is: 1 0 0 6 3 4 0 1 0 4 2 3 0 0 1 9 4 6 If 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 In the simplest form, isn't that a contradiction? ***If we want to change it into the simplest form of row, we must only carry out "row elementary transformation" instead of "column elementary transformation"? *** Thank you for your serious answer. If you have the Tongji version 4, you can see that the last element in line 2 of p61 example 1 is indeed - 2
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