Question

Each of the matrices given below is an augmented matrix of a system linear equations. In each case decide if the system has no solutions, exactly one solution, or infinitely many solutions. Try to perform as few computations as possible. A= ſi 2 0 1 Lo 0 1 3 0 1 1 0 1 1 1 0 B= ſi 0 0 3 47 0 1 3 1 1 LO 0 1 1 0 C= [100 0 1 0 Lo 0 1 D= [1 2 0 3 47 0 1 3 1 0 LO 0 0 0 2 E= [3 2 1 07 0 2 1 0 Lo 0 1 0 F= [1 2 17 0 0 0 LO 1 1] G= [i 20 31 0 0 0 0 LO 0 0 0 H= [2 0 LO 2 7 37 3 3 1 0 4 0

Answer 1

A = ri 2 1 117 LO 0 0 0 0 Here rank of coefficient matrix = rank of augmented matrix and rank of coefficient matrix is 2 but order of coefficient matrix is ux3. so, the above system has infinitely many solution. B: Ti 0 0 3 47 To 1 3 1 1 | Here rank of coefficient matrix is 3 with so, the above system has infinitely many a variables solution.

C = ſio 01 Loo!] tere runk of augmented matrix > rank of coefficient - matrix so, the above system has no solution. D = I2 347 o 1 3 1 0 Loo 0 0 2] Here runk of augmented matrix> rank of coefficient matrix no the above system than no solution. E = 53 21 01 Here the coefficient matrix is of full rank. So the above system has exactly one solution. F = ['217 0 0 0 F: Here renk of trefficient matrix = rouk of augmented matrix and is not of full rook. So, the above system than infinitely many solution 6 = [ 2 0 37 Loo 0 0 ] Here rank of augmented matrix = nuk of coefficient matrix and coefficient matrix is not of full rank. . so, the above system has infinitely many solution. 12 2 7 3 To 3 3 10 0 4 0 ] Here the coefficient matrix is of full rank. So, the above system has exactly one solution. H =