The Total solution for NCERT class 6-12
x + y – 2z = 0
2x + y – 3z =0
5x + 4y – 9z = 0
Answer - 1 : -
Given x + y – 2z = 0
Any system of equationcan be written in matrix form as AX = B
Now finding theDeterminant of these set of equations,
= 1(1 × (– 9) – 4 × (–3)) – 1(2 × (– 9) – 5 × (– 3)) – 2(4 × 2 – 5 × 1)
= 1(– 9 + 12) – 1(– 18+ 15) – 2(8 – 5)
= 1 × 3 –1 × (– 3) – 2× 3
= 3 + 3 – 6
= 0
Since D = 0, so thesystem of equation has infinite solution.
Now let z = k
⇒ x + y = 2k
And 2x + y = 3k
Now using the Cramer’srule
2x + 3y + 4z = 0
x + y + z = 0
2x + 5y – 2z = 0
Answer - 2 : -
Given
= 2(1 × (– 2) – 1 × 5)– 3(1 × (– 2) – 2 × 1) + 4(1 × 5 – 2 × 1)
= 2(– 2 – 5) – 3(– 2 –2) + 4(5 – 2)
= 1 × (– 7) – 3 × (–4) + 4 × 3
= – 7 + 12 + 12
= 17
Since D ≠ 0, so thesystem of equation has infinite solution.
Therefore the systemof equation has only solution as x = y = z = 0.
Answer - 3 : -
Find the real valuesof λ for which the following system of linear equations has non - trivialsolutions.
Also, find the non -trivial solutions
2λx - 2y + 3z = 0
x + λy + 2z = 0
2x + λz = 0
Answer - 4 : -
Answer - 5 : -