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W leite matrix equation of above system of equation Given system of equation : 2,+ 372 - 543 = 11 32, 222-1522 =10 23, -5X2 -10 23 - Step 1 : 3 -5 3-2 -15 2 -5 -16 22 a 9 Alsay) x(sqy) Besayo AXB .. step2 : Augmented matrix of above matrix equation [A : B] [A : B] = 3 - 2 3 -5 11 -IS : 10 -lo : 4 ] Step 3: Reduce augmented matrix in echelon for by elementary operation. 11 3 R₂ R2-3R 3 5 : 11 : -23 -110:-23 -10 : 9 Rzy R3 - 2R, : . U -5 11 -15 : 10 3 5 -11 R3 R3-R2 0 3 -2 co O : -13 2 -5 and Rank ( [A: B]) Step 4: find Rank(A) non zero zows 07 Rank of a matrix is number of column in echelon form. 2 non non Rank ( A ) = (Number of zero rows in echelon form) Rank ([A: B]) = 3 (Number of zero rows in echelon form) Step 5:.96 Rank(A) = Rank (LA: B3) Number of unknowns then the system of linear equation has unique solution of Rank(A) = Rank ( [A: B]) < Number of unknowns then the system of lineas equation has infinitely many Solutions.
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· 94 RONK(A) E Rank ( [A; B]) then the system of equation has no solution Nowe here Rank(A): 2, Rank : 3 Rank (A) F Rank ( [a: 8] ) Hence system of equation has no solution. CS Scanned with CamScanner
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