2 X 1 Column Matrix

These are the calculations.

2 x 1 column matrix.

The size or dimensions m n of a matrix identifies how many rows and columns a specific matrix has. We call the number 2 in this case a scalar so this is called scalar multiplication. Throughout boldface is used for the row and column vectors. The 1 2 entry is 0 the 2 3 entry is 1 and so forth.

The number of rows is m and the number of columns is n. In mathematics a matrix plural matrices is a rectangular array or table see irregular matrix of numbers symbols or expressions arranged in rows and columns. For another example if x is an n k 1 matrix and β is a k 1 1 column vector then the matrix multiplication xβ is possible. Note that the matrix multiplication ba is not possible.

A matrix is a rectangular arrangement or array of numbers often called elements. That is c is a 2 5 matrix. The resulting matrix c ab has 2 rows and 5 columns. The transpose indicated by t of a row vector is a column vector.

So if a is an m n matrix then the product a x is defined for n 1 column vectors x. For example since the entry 2 in the matrix above is in row 2 column 1 it is the 2 1 entry. Multiplying a matrix by another matrix. Similarly a row vector or row matrix is a 1 m matrix that is a matrix consisting of a single row of m elements.

The dot product is performed for each row of a and each column of b until all combinations of the two are complete in order to find the value of the corresponding elements in matrix c. A 2 4 1 2 ans 5 11 9 7 4 14. In general the i j entry of a matrix a is written a ij and the statement. For example when you perform the dot product of row 1 of a and column 1 of b the result will be c 1 1 of.

The dimension of a matrix must be known to identify a specific element in the matrix. In linear algebra a column vector or column matrix is an m 1 matrix that is a matrix consisting of a single column of m elements. A matrix this one has 2 rows and 3 columns to multiply a matrix by a single number is easy. A 2 4 extract the element in row 2 column 4 ans 8 more generally one or both of the row and column subscripts can be vectors.

The resulting matrix xβ has n rows and 1 column. Let us define the multiplication between a matrix a and a vector x in which the number of columns in a equals the number of rows in x. For example the dimension of the matrix below is 2 3 read two by three because there are two rows and three columns.