A matrix is a rectangular array of numbers. Entries are arranged in rows and columns.
The dimensions of a matrix refer to the number of rows and the number of columns. A [latex]3\times 2[/latex] matrix has three rows and two columns.
We add and subtract matrices of equal dimensions by adding and subtracting corresponding entries of each matrix.
Scalar multiplication involves multiplying each entry in a matrix by a constant.
Scalar multiplication is often required before addition or subtraction can occur.
Multiplying matrices is possible when inner dimensions are the sameāthe number of columns in the first matrix must match the number of rows in the second.
The product of two matrices, [latex]A[/latex] and [latex]B[/latex], is obtained by multiplying each entry in row 1 of [latex]A[/latex] by each entry in column 1 of [latex]B[/latex]; then multiply each entry of row 1 of [latex]A[/latex] by each entry in columns 2 of [latex]B,\text{}[/latex] and so on.
Many real-world problems can often be solved using matrices.
We can use a calculator to perform matrix operations after saving each matrix as a matrix variable.
Glossary
column
a set of numbers aligned vertically in a matrix
entry
an element, coefficient, or constant in a matrix
matrix
a rectangular array of numbers
row
a set of numbers aligned horizontally in a matrix
scalar multiple
an entry of a matrix that has been multiplied by a scalar
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