Here are the essential concepts you must grasp in order to answer the question correctly.
Matrix Multiplication
Matrix multiplication involves taking two matrices and producing a new matrix by multiplying rows of the first matrix by columns of the second. For two matrices A (m x n) and B (n x p), the resulting matrix C (m x p) is formed where each element C[i][j] is the dot product of the i-th row of A and the j-th column of B.
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Dimensions of Matrices
The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a 3x3 matrix has 3 rows and 3 columns. When multiplying matrices, the number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be valid.
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Dot Product
The dot product is a fundamental operation in linear algebra that combines two equal-length sequences of numbers (usually coordinate vectors) into a single number. In the context of matrix multiplication, the dot product is used to calculate each element of the resulting matrix by summing the products of corresponding entries from the row of the first matrix and the column of the second matrix.
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