The following questions are designed to explore the dimensions of matrices and what you can and can't do with matrices of differing dimensions.
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\nFor $\\var{Dimensions}$ there are $\\var{rows[0]}$ rows and $\\var{columns[0]}$ columns. We write this as \"this is a $\\var{rows[0]}$X$\\var{columns[0]}$ matrix\".
\nTwo Matrices can be added or subtracted if they have the exact same dimensions as each other. For example $\\var{canadd1}$ and $\\var{canadd2}$ are both $\\var{rows[1]}$X$\\var{columns[1]}$ matrices and therefore can be added (or subtracted). However, $\\var{cantaddsub1}$ is a $\\var{rows[3]}$X$\\var{columns[3]}$ matrix and $\\var{cantaddsub2}$ is a $\\var{rows[3]}$X$\\var{columns[3]+1}$ matrix. Since these dimensions are different these matrices cannot be added or subtracted.
\nWhen you multiply two matrices together the number of columns in the first matrix must match the number of rows in the second matrix. For example in the calculation $\\var{Mult3}$X$\\var{Mult4}$ the first matrix has $3$ columns and the second matrix has $3$ rows so they can be multiplied. In addition to this when multiplying two matrices (that can be multiplied) the result will be a single matrix that has the number of rows of the first matrix and the number of columns of the second matrix. In this example the first matrix has $\\var{rows[0]}$ rows and the second matrix has $\\var{columns[1]}$ columns, so the result of multiplying the two matrices will be a $\\var{rows[0]}$X$\\var{columns[1]}$ matrix.
\nUse this link to find some resources which will help you revise this topic.
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\n$\\var{dimensions}$
\n[[0]]X[[1]]
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\n(Indicate ALL possible answers by ticking the corresponding box(es))
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\n$\\var{Mult1}$X$\\var{Mult2}$
\n[[0]]
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\n$\\var{Mult3}$X$\\var{Mult4}$.
\n\n[[0]]X[[1]]
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