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.
Gaussian elimination से हम इस सिस्टम को हल करके उन \(\lambda\) के मान निकाल सकते हैं जिनके लिए यह सिस्टम consistent हो। ### Step 1: सिस्टम को स्टैंडर्ड फॉर्म में लिखें दी गई समीकरणों को सामान्य रूप में लिखते हैं: 1. \( x - 3y + 4 = 0 \) \[ x - 3y = -4 \] 2. \( 3x - 2y = __________ _______ ____ ______ ________ _______ ___ _______ _______ ____ __________.
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Express in standard (algebraic) form. Further, give an Argand diagram
in which and
are plotted
Obtain the discriminant of the equation Hence provide the nature of its roots
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.
ii) (A\B) UC=A\(B∩C) for any three sets A, B and C.
iii) If ze R, then |z|=z.
iv) xm + a1 xm -1+ ....am-1 x + am = 0, ai ∈ R∀ i = 1, ..., m, has a root in R only if m is an odd number.
v) x > 0 is necessary for x+3>1.
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 > 4, the AM of the first n natural numbers is greater than n +1.
Solve by substitution, the system you have obtained in 5(a).
Show that
Prove that
two non-zero, 3×3 matrices A and B , with