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Math 105II – Systems of Linear Equations6. Solve the following systems of linear equations using Gaussian elimination.a) x + 2y= 7 b) x − 3y= 5c) − x + 2y= 1.5d)g)2x+ y = 8− 3x + 5y= −2e)3x+ 4y= 4− 2x+ 6y= −10x − 3x= −2f)− 2x= 54x− 8y= 32 2x1+ 2x2+ x3= 4x + 2y+ z = 8 h) 2x + y + 2z= 7− 3x− 6y− 3z= −21x + y + 2z= 4j) 3x + 3y + 12z=x + y + 4z= 22x + 5y + 20z= 10− x + 2y + 8z=6413x+ x122x − 2y − 4z= 4k) 2x − 3y + 4z − t =336x + y − 3z + 2t=−2x − 4y + 7z − 3t=4x − y − 2z + 3t=822x− 4y= 3x + x − 5x= 31x12− 2x= 12x1− x2− x3= 0i) x − 2y + 4z=3362x − 4y + 10z= 18− 3x + 6y − 9z= −97. Solve the systems of linear equations in 6 using the Gauss-Jordan method.8. Solve the following homogeneous systems of linear equations by any method.a) x− y+ z = 0x + x + x = 0 c) x + 2y + z + w=0x+ y = 0x+ 2y− z = 0b)1 2 3−2x −2x − 2x= 01 2 33x + 3x + 3x= 01 2 39. Solve the following systems on nonlinear equations.a)1 1 1x− 2y+z= 1b) x − z =−11 1 12x+ 2y− 3z= 101 13x+z= 8y2x + 2e + 5 z = 21− + =yx e zx − y + w=0y − z + 2w=010. Find values of a, b and c (if possible) such that the given system of linear equations hasi) a unique solutionii) no solutioniii) an infinite number of solutionsa) x + y + = 2b) x + y + = 0xy + z = 2+ z = 2ax + by + cz = 0xy + z = 0+ z = 0ax + by + cz = 04Winter 2006 Martin Huard 2