Q2 of 75 Page 8

Solve the following systems of homogeneous linear equations by matrix method:

2x – y + 2z = 0


5x + 3y – z = 0


X + 5y – 5z = 0

The system can be written as



A X = 0


Now, |A| = 2(– 15 + 5) + 1(– 25 + 1) + 2(25 – 3)


|A| = – 20 – 24 + 44


|A| = 0


Hence, the system has infinite solutions


Let z = k


2x – y = – 2k


5x + 3y = k



A X = B


|A| = 6 + 5 = 11≠0 So, A – 1 exist


Now adj A = =


X = A – 1 B =


X =


Hence, x = , y = and z = k


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21

A shopkeeper has 3 varities of pens ‘A’, ‘B’ and ‘C’. Meenu purchased 1 pen of each variety for a total of ₹21. Jeen purchased 4 pens of ‘A’ variety, 3 pens of ‘B’ variety and 2 pens of ‘C’ variety for ₹60. While Shikha purchased 6 pens of ‘A’ variety, 2 pens of ‘B’ variety and 3 pens of ‘C’ variety for ₹70. Using matrix method find the cost of each pen.

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Solve the following systems of homogeneous linear equations by matrix method:

 3

Solve the following systems of homogeneous linear equations by matrix method:

3x – y + 2z = 0


4x + 3y + 3z = 0


5x + 7y + 4z = 0

 4

Solve the following systems of homogeneous linear equations by matrix method:

x + y – 6z = 0


x – y + 2z = 0


– 3x + y + 2z = 0