Differentiate between consistent and Inconsistent system of linear equations. (2 Marks) b.) Discuss the consistency of...

 

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Differentiate between consistent and Inconsistent system of linear equations. (2 Marks) b.) Discuss the consistency of the following system of equations and solve it, (12 Marks) i.) x +2y- z = 1 2x + y + 4z = 2 3x + 3y + 4z = 1 ii.) x+y+2z = 9 2x + y+ 2z = 1 3x + 6y- 5z =0 iii.) 2x - y = 5 x + 3y = 1 4x - 7y= 2 c.) i.) Show that the set of vectors In are linearly independent if X1, X2,..., and only if the equation - α1x1, A2X2, ..., An Xn only one solution a₁ =a₂ =...=an = 0 (3 Marks) 0 has one and ii.) Prove that the function cost and sine are linearly independent in the space [0, 2π] of continuous functions. (3 Marks) Differentiate between consistent and Inconsistent system of linear equations. (2 Marks) b.) Discuss the consistency of the following system of equations and solve it, (12 Marks) i.) x +2y- z = 1 2x + y + 4z = 2 3x + 3y + 4z = 1 ii.) x+y+2z = 9 2x + y+ 2z = 1 3x + 6y- 5z =0 iii.) 2x - y = 5 x + 3y = 1 4x - 7y= 2 c.) i.) Show that the set of vectors In are linearly independent if X1, X2,..., and only if the equation - α1x1, A2X2, ..., An Xn only one solution a₁ =a₂ =...=an = 0 (3 Marks) 0 has one and ii.) Prove that the function cost and sine are linearly independent in the space [0, 2π] of continuous functions. (3 Marks)