Texas Instruments TITANIUM TI-89 - Manual (Page 863)

Appendix A: Functions and Instructions 863
real( list1 )
⇒ ⇒ ⇒ ⇒ list
Returns the real parts of all elements.
real({a+iù b,3,i}) ¸ {a 3 0}
real( matrix1 )
⇒ ⇒ ⇒ ⇒ matrix
Returns the real parts of all elements.
real([a+iù b,3;c,i]) ¸
[
a 3
c 0
]
4444Rect
MATH/Matrix/Vector ops menu
vector 4444Rect
Displays vector in rectangular form [x, y, z]. The
vector must be of dimension 2 or 3 and can be a
row or a column.
Note: 4444Rect is a display-format instruction, not a
conversion function. You can use it only at the
end of an entry line, and it does not update
ans .
Note: See also 4 Polar .
[3,pà4,pà6]4Rect ¸
[
3ш ‡2
4
3ш ‡2
4
3ш ‡3
2
]
[a,b,c] ¸ [aø cos(b)ø sin(c)
aø sin(b)ø sin(c) aø cos(c)]
complexValue 4444Rect
Displays complexValue in rectangular form a+b i .
The complexValue can have any complex form.
However, an r e i q entry causes an error in Degree
angle mode.
Note: You must use parentheses for an (r q)
polar entry.
In Radian angle mode:
4 e ^(p/3)4Rect ¸ 4ø e
p
3
(4p/3)4Rect ¸ 2+2ш 3 ш i
In Gradian angle mode:
(1100)4Rect ¸ i
In Degree angle mode:
(460)4Rect ¸ 2+2ш
3333 ш i
Note: To type
4444Rect from the keyboard, press
2  for the 4444 operator. To type , press
2 ’ .
ref()
MATH/Matrix menu
ref( matrix1 [, tol ]) ⇒ ⇒ ⇒ ⇒ matrix
Returns the row echelon form of matrix1 .
Optionally, any matrix element is treated as zero
if its absolute value is less than
tol . This tolerance
is used only if the matrix has floating-point
entries and does not contain any symbolic
variables that have not been assigned a value.
Otherwise,
tol is ignored.
• If you use ¥ ¸ or set the mode to
Exact/Approx=APPROXIMATE , computations
are done using floating-point arithmetic.
• If tol is omitted or not used, the default
tolerance is calculated as:
5 E л 14 щ max(dim( matrix1 ))
ù rowNorm( matrix1 )
Note: See also rref().
ref([л2,л2,0,л6;1,л1,9,л9;л5,
2,4,л4]) ¸





 1 л 2/5 л 4/5 4/5
0 1 4/7 11/7
0 0 1 л 62/71
[a,b,c;e,f,g]!m1 ¸
[ ]
a b c
e f g
ref(m1) ¸








1
f
e g
e
0 1
aøgì cøe
aøfì bшe