FINAL_TEST_11_final (1).pdf - Q-1(5 2=7 Marks Consider the system x1 \u2212 x2 \u2212 x3 \u2212 2x4 = 0 2x1 x2 x3 2x4 = 3 3x1 x2 \u2212 x3 \u2212 4x4 = 6 a Solve by

FINAL_TEST_11_final (1).pdf - Q-1(5 2=7 Marks Consider the...

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Q-1) (5+2=7 Marks) Consider the systemx1-x2-x3-2x4= 02x1+x2+x3+ 2x4= 33x1+x2-x3-4x4= 6a) Solve by Gauss-Jordan elimination.b) Find a particular solution in whichx2= 3. 1
Q-2) (4+3=7 Marks) LetA=31-1201,B=1-112, C=1-10315, D=-1002Compute:a) tr(CA+ 2D5)b) 9 2
Q-3) (4+2=6 Marks) ConsiderA=123102211.a) Find A-1,by using theadj(A). No marks will be given for other methods used.b) Solve the system using the inverse matrixx+ 2y+ 3z= 1x+ 2z= 22x+y+z= 3 3
Q-4) (4 Marks) Determine the values ofafor which the system has1) exactly one solution;2) no solution;3) infinitely many solution,x+ 5y= 13x+ (a2-1)y=a-1 4
Q-5)(4 Marks) Find the elementary matricesE1E2,such thatI=E2E1A,whereA=1032Q-6) (4 Marks) Find A from(I+ 2A)-1=1423 5

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