Row Matrix
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A row matrix, also known as a row vector, is a matrix with only one row and multiple columns. It can be represented in the form [a1, a2, a3, …, an], where a1, a2, a3, …, an are the elements of the row matrix.
For example, the row matrix [2, 4, 6] has one row and three columns. It can also be represented as a 1×3 matrix.
Row matrices can be added or subtracted from one another if they have the same number of columns. The addition or subtraction is performed by adding or subtracting the corresponding elements in each matrix. For instance, the row matrices [1, 2, 3] and [2, 3, 4] can be added as [1+2, 2+3, 3+4] = [3, 5, 7].
In linear algebra, row matrices are often used to represent variables in a system of linear equations. The coefficients of the variables can be organized in a row matrix, and the matrix can be used to solve the equations using methods such as Gaussian elimination or matrix inversion.
Row matrices can also be multiplied by column matrices, which are matrices with one column and multiple rows. The multiplication is performed by multiplying each element in the row matrix by the corresponding element in the column matrix and adding the products together. For example, the row matrix [2, 4, 6] can be multiplied by the column matrix [1, 2, 3] as 2×1 + 4×2 + 6×3 = 28.
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