Maximizing Efficiency: Utilizing a Pressure Cooker for Cooking

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SUMMARY

The discussion centers on the conditions required for matrix multiplication, specifically focusing on matrices P and Q with dimensions w × x and y × z, respectively. For the product PQ to be defined, the number of columns in matrix P (x) must equal the number of rows in matrix Q (y). The resulting matrix from this multiplication will have dimensions corresponding to the number of rows in P and the number of columns in Q, which is 2x3 in this case. Additionally, the concept of matrix transposition is introduced, where A^T and B^T represent the transposed versions of matrices A and B, respectively.

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Homework Statement
Anyone who understands this?
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I think it has something to do with multiplying matrix A and B? But I can't figure out.
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If matrix ##P## has dimensions ##w \times x## and matrix ##Q## has dimensions ##y \times z##, what is the condition for the product ##PQ## to be defined? Think in terms of rows and columns...
 
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The new matrix will be 2x3..

But I still can't understand it ://
 
What is the relationship between the number of columns in the matrix on the left and the number of rows in the matrix on the right, when they’re multiplied together?
 
conv said:
The new matrix will be 2x3..

But I still can't understand it ://

Why don't you try to calculate the matrix ##C## in each case? See which ones you can do and which ones you can't.
 
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I can't find out how to do that in my book. Have tried for a long time now.
What does the A^T and B^T represent?
 
If the general entry is described by ##A=(a_{ij} )##, where i is the ith column and j is the jth row, then ##A^{T}:=(a_{ji})## , meaning a flip of rows and columns in the original matrix ( The one with Keanu, I think; ) ).
 
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