HP 10413 Datasheet download pdf (Page 273)

273

INVERSE(matrix)

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 the

hp 39g+ on page 172 and 288.

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 hp 39g+ 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

the non-fractional matrix.

i.e.

23 5 3

45 4 2

−

  

=⇒=

  

−

  

Remember that the inverse matrix is not just

the matrix, but the fraction times the matrix.

See also: RREF

, DET

LQ(matrix)

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.

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HP 10413 Datasheet Page 273

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