 Hello friends, welcome to the session. I am Alka. We are going to discuss matrices. Our given question is a trust fund has rupees 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year and the second bond pays 7% interest per year. Now using matrix multiplication determine how to divide rupees 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of A rupees 1800 B rupees 2000. So now let's start with the solution. If investment is given as a matrix A which is equal to matrix A X and 30,000 minus X. Now we know interest paid by first bond equal to 5% that is 0.05 and interest paid by second bond equal to 7% which is 0.07. Therefore interest is given by the matrix B where B equal to matrix 0.05 and 0.07. Now we will calculate the total interest of both the bonds which is given by AB which is equal to matrix X 30,000 minus X multiplied by matrix 0.05 and 0.07 which is equal to X into 0.05 plus 30,000 minus X into 0.07 matrix. This is equal to matrix 0.05 X plus 2100 minus 0.07 X which is equal to 2100 minus 0.02 X. Now according to our question when if the trust fund must obtain an annual total interest of rupees 1800 that is total interest obtained equal to rupees 1800 and from above we can see say that 2100 minus 0.02 X equal to 1800. This implies minus 0.02 X equal to 1800 minus 2100 this implies minus 0.02 X equal to minus 300 minus minus get cancel out. This implies X equal to 300 upon 0.02 this implies X equal to 15,000 hence money invested in first bond equal to rupees 15,000 and money invested in second bond equal to rupees 30,000 minus 15,000 that is equal to 15,000 rupees. Now we will see the second part where the total interest obtained equal to rupees 2000. Now 2100 minus 0.02 X equal to 2000 this is equal to minus 0.02 X equal to 2000 minus 2100. This implies minus 0.02 X equal to minus 100 minus minus get cancel out this implies X equal to 100 upon 0.02 this implies X equal to 5000 hence money invested in first bond equal to rupees 5000 and money invested in second bond equal to rupees 30,000 minus 5000 which is equal to rupees 25,000. So hope you understood the solution and enjoyed the session. Goodbye and take care.