12th Maths Guide Solution Application of Matrices and Determinants Exercise 1.5

Question no 1:- Solve the following systems of linear equations by Gaussian elimination method.

(i) 2x – 2y + 3z = 2, x + 2y – z = 3, 3x – y + 2z = 1

Solution:

(ii) 2x + 4y + 6z = 22, 3x + 8y + 5z = 27, -x + y + 2z = 2

Solution:

Question no 2:- If ax² + bx + c is divided by x + 3, x – 5, and x – 1, the remainders are 21, 61 and 9 respectively. Find a, b and c. Use Gaussian elimination method.

Solution:-

Question no 3:- An amount of Rs 65,000 is invested in three bonds at the rates of 6%, 8% and 10% per annum, respectively. The total annual income is Rs 5,000. The income from the third bond is Rs 800 more than that from the second bond. Determine the price of each bond. Use Gaussian elimination method.

Solution:-

Question no 4:-A boy is walking along the path y = ax² + bx + c through the points (-6, 8),(-2, -12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? Use Gaussian elimination method.

Solution:-