For example, a MATLAB session to compute theĪs we have seen, a determinant is not the same as a matrix, but a determinantĬan be found from a matrix. Then use the det function to evaluate the determinant. Rules exist to evaluate n x n determinants by hand, but we can use MATLAB to do this. The rule for reducing a 2 x 2 determinant to a single number A determinant having two rows and two columns is aĢ x 2 determinant. Vertical bars are used to denote a determinant, whereas square brackets denote a matrix. The matrix A has m rows and n columns, so its dimension is expressed as m x n.ĭeterminants are useful for finding out whether a set of equations has a solution. A determinant is a special square array that, unlike a matrix, can be reduced to a single number. In general, the set of m equations in n unknown Vector b contains the right sides of (6.2-1) and (6.2-2).

The vector x contains the variables X1 and X2, and the and the second row contains the coefficients Note that the first row in A consists of the coefficients of The matrix A corresponds in an ordered fashion to the coefficients of X1 and X2 Usually, when printed in text, lowercase boldface letters denote a vector, and uppercase boldface letters denote a matrix. Matrix notation enables us to represent multiple equations as a single matrix equation.

In this chapter a vector is taken to be a column vector unless otherwise specified. A vector is a special case of a matrix that has either one row or one column. This section describes the use of matrix notation.Īs you saw in Chapter 2, a matrix is an ordered array of rows and columns containing numbers, variables, or expressions. Sets of linear algebraic equations can be expressed in matrix notation, a standard and compact method that is useful for expressing solutions and for developing software applications with an arbitrary number of variables.

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