Page 167 - الرياضيات المتقدمة كتاب الطالب للصف 11 الفصل 1

b Gb ^ Æar© {6 1.b d?Wb ç 2;N x- 'b X?cb f Ÿ .[ gb zB y2b

¦ UrV>fa 40-i . fa
,1Vfa
Ø
matrix E b60: ± »C/ Ò –`= b ^ ±¹ ³P: ­Ò Ëb6j ^8 c9 _=7 D= R C< ? matrix E b60: ± ËR4
´C b60: ± ÏP ˜ ^ X a ËR C<= ¯ S R Ò “C< C= Ò­’ C< R E b60: ± c ¯
element R0;4 ±
d »C 8 „±Ò –½C84 „± ^ E= C= ± û ±b: ±Ò ´C7= 2 ± ` P P4 ± d Z ±Ò ÌC2 c9
rows Ëb6j ^= : ´C b60: ± ϱP ± `8: C: ˜E b ± ³R/; ± ´„C: „ E= b C ¶ºC: Ò­ Ïb »

columns ³P: ­ ˜¹C4 M± d Z b ´C= ±P ¯ ^ ´C b94

E b60: ± E » EjC ñb ­Ò –E b60: ± ½b84 Ò –´C b60: ± c9 ´C=9:4 ± c9 ³P b ± ÑQ d S R;
order of a matrix ˜E= Š± ´„¹C4: ± Û^ d C< ±P ± E=6= Ò –´C b60: ± `
E4 R E b60
oybM ybfNa q UrV>fa ›—
square matrix
E R6j E b60 UrV>fa 0

zero matrix .columns ³P: ­Ò rows Ëb6j d E R Ðb8 E b60: ± ^ ±¹ RjC;4 ± y
³P C E b60: ±
˜³P: ­ Ð Ò Ëb6j Ï c9 Ôb C< A –“Ð ” ϒ C< » E b60: ± C; P ÐC ±º¯ y
identity matrix £ £
E b60: ± ¹P ² ² Л œ› ›› ² ² =

² М œœ ›œ ²
determinant of a ² ²
¤ Ð Ï ¤
œ
›
matrix Ï Ï ÎÓÓ
Õ
³¹R6;: ± E b60: ± ¹b b R0;4 ± Э c ¯ R=/ Õ : –C<= element ±R0; ^ :Ù E b60: ± ^ ±¹ Ð Ï Û^
›œ
˜ÎÒM± ¹b:4 ±Ò d C ± û0 ± d
singular matrix
£ ² - £
E b60: ± R ­ order of a matrix E b60: ± E » .( × œ’ E R ± ` E b60 d ² ² › ž œ ² Ò
²
²
² ²
³¹R6;: ± R= ¤ › š  ¤
˜²R1 ±Ò ·R2 ±Ò Z: ± ´C=9: «±R ¯ P; _<
non-singular matrix
ûj E b60 UrV>fa L ri
row matrix ¤C<; ñb ­ ³P ´C b60:9
¹b: E b60
( × ›’ E R ± ` E b60 d Ò “ Ÿ œ’ ^ ûj E b60 —›
column matrix
£ œ £
³¼S4: ± E b60: ± ² ²
²
²
.(› × ’ E R ± ` E b60 d Ò Ÿ E b60: ± ^ ¹b: E b60 — œ
² ²
augmented matrix ² ²
¤ ¤
E b60: ± ½b84 –³P: M± ` Ð C< Ò –Ëb60 ± ` Ð C< E b60 d ¤square matrix E4Û R: ± E b60: ± -
£ £
inverse matrix ² Л œ› ›› ²
² ¤d E C4 ± C< »bjÒ
²
² М œœ ›œ ²
² ²
¤ Ð Ð ¤
œÐ ›Ð
–±Õ»C6j­ C RjC; Z=: Ðb8 d ± E b60: ± d ¤zero matrix E R60 ± E b60: ± -ž
˜E » Û Ô­ ` E b60: ± ÑQ Ðb8 Э `8: Ò