Q1 of 75 Page 8

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

2x – y + z = 0


3x + 2y – z = 0


X + 4y + 3z = 0


The system can be written as



A X = 0


Now, |A| = 2(6 + 4) + 1(9 + 1) + 1(12 – 2)


|A| = 2(10) + 10 + 10


|A| = 40 ≠ 0


Since, |A|≠ 0, hence x = y = z = 0 is the only solution of this homogeneous equation.


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A total amount of ₹7000 is deposited in three different saving bank accounts with annual interest rates of 5%, 8% and respectively. The total annual interest from these three accounts is ₹550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.

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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:

2x – y + 2z = 0


5x + 3y – z = 0


X + 5y – 5z = 0

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

3x – y + 2z = 0


4x + 3y + 3z = 0


5x + 7y + 4z = 0