Is Cramer’s Rule applicable for solving the linear system below? If yes, apply it.
Otherwise, alter the last equation in the system so that the solution can be obtained
by applying the Rule.
x + y + z = π
− πx + πy +sqrt(2z) = 0
π2 x + π2 y + 2z = 0 .
__________ ___ ________ _______ _________ ________ ___.
__________ ________ _______ __________ __________.
_____ ____ _______ ____ _________ ___.
______ _______ ________ ____ ____ ________ _________ ____ ____ _____ ______ ____.
________ _____ ____ _____ ____ __________ ___ __________ _____ ___.
_________ ______ _________ _______ _________ _________.
___ ______ _________ _____ ___ _______ ___ ______ ________ _____ __________ __________.
__________ ____ __________ __________ ___ ____ _____ ____ _______.
_________ _____ _________ ____ ________.
____ _______ _____ ________ ___ _____.
_________ ________ ______ ________ ____ _______ ___ ___.
__________ ___ __________ _________ ______ _________.
________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
Apply the Gaussian elimination process to determine values of λ for which the following linear system is consistent:
x − 3y + 4 = 0, 3x − 2y = λ, y = 6 − 2x .
Is Cramer’s Rule applicable for solving the linear system below? If yes, apply it.
Otherwise, alter the last equation in the system so that the solution can be obtained
by applying the Rule.
x + y + z = π
− πx + πy +sqrt(2z) = 0
π2 x + π2 y + 2z = 0 .
Solve x4 − 8x3 + 21x2 − 20x + 5 = 0 given that the sum of two of its roots is 4.
For any two sets A and B , in a universal set U , prove that
A ⊆ B ⇔ A ∪ B = B .
Solve by substitution, the system you have obtained in 5(a) .
Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that ‘{1, padma, blue} is a set’ is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
iii) If z ∈ R , then | z | = z .
vi) Any system of three linear equations in two variables has no solution.
vii) If a matrix has n2 entries, where n ∈ N , then it is a square matrix.
viii) For n > 2 , the AM of the first n natural numbers is greater than n + 1.