Maximizing Efficiency: Utilizing a Pressure Cooker for Cooking

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For the product of matrices P and Q to be defined, the number of columns in matrix P must equal the number of rows in matrix Q. The resulting matrix will have dimensions based on the rows of P and the columns of Q. Users express confusion about calculating the resulting matrix and the concept of transposition. The transpose of a matrix A, denoted A^T, involves flipping its rows and columns. Understanding these concepts is crucial for maximizing efficiency in matrix operations.
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Homework Statement
Anyone who understands this?
Relevant Equations
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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