HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 197

INVERSE() This function produces the inverse matrix of an n x n square matrix, where possible. A fully worked example of the use of an inverse matrix to solve a 3 by 3 system of equations is given in the chapter on Using Matrices on page 211 and in Appendix A on page 302. An error message is given (see right) when the matrix is singular (det. zero). Note: Some people write the inverse matrix as a fraction (one over the determinant) multiplied by a matrix, so as to avoid decimals and fractions within the inverse matrix. The calculator does not do this. If you want the matrix with the determinant factored out, then evaluate DET(matrix) first, record the fraction and then evaluate DET(matrix) * INVERSE(matrix) to obtain (usually) a non-fractional matrix. i.e. A = ⎡ 2 ⎣⎢4 3⎤ 5⎦⎥ ⇒ A−1 = 1 − 2 ⎡ 5 ⎣⎢−4 − 3 ⎤ 2 ⎥ ⎦ Remember that the inverse matrix is not just the matrix, but the fraction times the matrix. See also: RREF, DET LQ() This function takes an mxn matrix, factors it and returns a list containing three matrices which are (in order): • an mxn lower trapezoidal matrix • an nxn orthogonal matrix • an mxm permutation matrix. If you want to separate these matrices for later use then you should store them into a list variable. For example, if M1 was [[1,2,3],[4,5,6],[7,8,9]] then LQ(M1) L1 would store the three resulting matrices into list variable L1. In the HOME view you could now enter L1(1) M2 to store the first of the result matrices into M2 and so on. 197