(a) Solve the following systems of linear equations and determine whether the system is consistent or...

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(a) Solve the following systems of linear equations and determine whether the system is consistent or inconsistent: i. ii. iii. I + 13 =y = 3x 5263 2.5x+0.75 3y = 0 1.6x = 1.08 1.2y - I +== 7 30 2-r -18 4-9 (4 marks) (4 marks) (4 marks) (10 marks) (b) Use Gauss-Jordan Elimination method only to solve the following system for x, y and z. 2y+x+32 1 52+5y+2x=-3 = 2 3x 5y+11z (c) Find all solutions of the system whose augmented matrix has been reduced to 1 2 0 4 007 001 200-2 0 0 0 0 1 0 4 0 0 0 0 0 1 3 0 0 0 0 0 0 k (7 marks) (d) Express the following quadratic form as "sum of squares" by congruent trans- formation and write down the corresponding linear transformation - Q(x1, x2, x3)=10x+x²+x²-6x1x2 − 2x2x3 + x3x1. (a) Solve the following systems of linear equations and determine whether the system is consistent or inconsistent: i. ii. iii. I + 13 =y = 3x 5263 2.5x+0.75 3y = 0 1.6x = 1.08 1.2y - I +== 7 30 2-r -18 4-9 (4 marks) (4 marks) (4 marks) (10 marks) (b) Use Gauss-Jordan Elimination method only to solve the following system for x, y and z. 2y+x+32 1 52+5y+2x=-3 = 2 3x 5y+11z (c) Find all solutions of the system whose augmented matrix has been reduced to 1 2 0 4 007 001 200-2 0 0 0 0 1 0 4 0 0 0 0 0 1 3 0 0 0 0 0 0 k (7 marks) (d) Express the following quadratic form as "sum of squares" by congruent trans- formation and write down the corresponding linear transformation - Q(x1, x2, x3)=10x+x²+x²-6x1x2 − 2x2x3 + x3x1.

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a i The given system of linear equations can be written as 5x 12y 4z 8 13x 3y 0 To solve this system we can use the method of elimination Multiply the second equation by 4 52x 12y 0 Now subtract the s... View the full answer