Worksheet : Clss XII Mtries & Determinnts Prepred B:Mr. durhimn K Mth Teher l-hej Interntionl Shool, Jeddh (IGCSE). rhmnrk@gmil.om #00966007900# MTHEMTICS WKSHEET I Nme: Mrh 0. If 8 LGEBR (Mtries nd Determinnts) Mrks 0, write the minor of the element. [ ] 6. If, write the vlue of. 7 9 [ ] osθ sinθ sinθ osθ. Simplif: osθ sin. sin os θ os sin θ θ θ θ [ ]. Using properties of determinnts, prove tht q r r p p q q r p. [ ]. Using mtries, solve the following sstem of liner equtions. [ 6 ] 7; ; ; Using elementr opertions, find the inverse of the following mtri:.
Mrh 0 6. For mtri, [ ] ij Worksheet : Clss XII Mtries & Determinnts i, whose elements re given ij, write the vlue of. [ ] j 7. For wht vlue of, the mtri is singulr? [ ] 8. Write for. [ ] 9. Using properties of determinnts, prove tht. [ ] Using properties of determinnts, solve the following for : 8 9 7 6 6 0. 0. Using mtri method, solve the following sstem of equtions: 0 6 6 9 0 ; ; ;,, 0. [ 6 ] Using elementr trnsformtion, find the inverse of the mtri 0 0
Worksheet : Clss XII Mtries & Determinnts Foreign 00 (SET ). Write squre mtri of order, whih oth smmetri nd skew smmetri. [ ]. Wht is the vlue of the following determinnt? [ ]. From the following mtri eqution, find the vlue of the : [ ] 6. Prove the following, using properties of determinnts: ) (. [ ] Find the inverse of using elementr trnsformtions.. If, find. Using. Solve the following sstem of equtions: [ 6 ] ; 6; Foreign 00 (SET ) 6. From the following mtri eqution, find the vlue of : [ ] 6 7. Prove the following, using properties of determinnts: [ ] ) (
Worksheet : Clss XII Mtries & Determinnts Find the inverse of the following mtri, using elementr trnsformtions: 7 8. Using mtries, solve the following sstem of equtions: [ 6 ]. 6; ; Foreign 00 (SET ) 9. If, 9 find the vlue of. [ ] 0. Prove the following, using properties of determinnts: [ ] ( ) w v u p q d w v u q p d q p d ll Indi 00 (SET ). Wht positive vlue of mkes the following pir of determinnts equl? [ ] 6,. Write the djoint of the following mtri: [ ]. squre mtri of order nd 7. Write the vlue of dj.. [ ]. Epress the following s the sum of smmetri nd skew smmetri mtri, nd verif our result: [ ]. Using properties of determinnts, prove the following: [ 6 ] ( )( )( )( ). p p p p
Worksheet : Clss XII Mtries & Determinnts Find the inverse of the following mtri using elementr opertions: 0 0 ll Indi 00 (SET ) 0 6. If, then find the vlue of I. [ ] 0 ll Indi 00 (SET ) I I 7. For the following mtries nd B, verif tht ( ) I B B. [ ], B ( ) 8. Using mtries, solve the following sstem of equtions: [ 6 ] ; ;. If,, re positive nd unequl, show tht the following determinnt is negtive Delhi 00 (SET ) osα sinα 9. If, then for wht vlue of α is n identit mtri? [ ] sinα osα
Worksheet : Clss XII Mtries & Determinnts 0 0 0. Wht is the vlue of the determinnt? [ ] 6 7. If, then write the vlue of k. k [ ]. Using elementr row opertions, find the inverse of the mtri: [ ]. Using properties of determinnts, show the following: [ 6 ] ( ) ( ) ( ) ( ) Delhi 00 (SET ) Find the minor of the element of seond row nd third olumn ( ) 6 Delhi 00 (SET ) 0 7 [ ] in the following determinnt:. If is squre mtri of order nd k, then write the vlue of k. [ ] SY 0. If, find the vlue of? [ ] 6. If is n invertile mtri of order nd, then find the vlue of dj? [ ] 6 7. For wht vlue of is the mtri singulr? [ ] 8. Using properties of determinnts, prove the following [ ] ( )( )( )
Worksheet : Clss XII Mtries & Determinnts 9. If, find. Using. Solve the following sstem of equtions: [ 6 ] ; ; EXTR QUESTIONS 0. If, show tht. 9 [ ]. If, show tht 0 I [ ]. If nd ( ) B, verif tht ( ). T T T B B [ ]. If nd 7 0 B, find I B [ ]. If ( ) 7 f nd,find ( ) f [ ]. Construt mtri whose elements re ( ) j i ij. [ ] 6. Prove tht ( ) [ ] 7. Prove tht ( )( )( )( ). [ ] 8. Using properties of determinnts, prove tht: ( )( ) [ ]
9. Using properties of determinnts, prove tht: α β γ α β γ β γ α Worksheet : Clss XII Mtries & Determinnts γ α β 0. Prove tht. ( α β )( β γ )( λ β )( α β γ ) [ ] [ ]. Using properties of determinnts, prove tht: [ ] α β 0; where α, β. γ re in P. γ. Using mtries, solve the following sstem of equtions: 0; 0;. [ 6 ]. Solve the following sstem of eqution using mtri method: ; 7; 7. [ 6 ] Prepred B:Mr. durhimn K Mth Teher l-hej Interntionl Shool, Jeddh (IGCSE). rhmnrk@gmil.om #00966007900#