Ex 4.6, 4 - Chapter 4 Class 12 Determinants (Term 1)

Transcript

Ex 4.6, 4 Examine the consistency of the system of equations. x + y + z = 1 2x + 3y + 2z = 2 ax + ay + 2az = 4 Simplifying 3rd equation ax + ay + 2az = 4 a(x + y + 2z) = 4 x + y + 2z = 4/𝑎 Now System of equation is x + y + z = 1 2x + 3y + 2z = 2 x + y + 2y = 4/𝑎 Writing equation as AX = B [■8(1&1&[email protected]&3&[email protected]&1&2)] [■8(𝑥@𝑦@𝑧)] = [■8([email protected]@4/𝑎)] Hence, A = [■8(1&1&[email protected]&3&[email protected]&1&2)] , X =[■8(𝑥@𝑦@𝑧)] & B =[■8([email protected]@4/𝑎)] Calculating |A| |A| = |■8(1&1&[email protected]&3&[email protected]&1&2)| = 1 |■8(3&[email protected]&2)| –1 |■8(2&[email protected]&2)| +1|■8(2&[email protected]&1)| = 1(6 – 2) – 1(4 – 2) + 1 (2 – 3) = 4 – 2 – 1 = 1 ≠ 0 Since |A| ≠ 0 Hence system of equation is consistent