Q18 of 108 Page 80

If and I is the identity matrix of order 2, show that

We know that I

Now, LHS = I + A



And on RHS = (I – A)








= LHS


Hence Proved.


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If, prove that A3 – 6A2 + 7A + 2I = 0

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If , find k so that A2 = kA – 2I

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A trust fund has Rs. 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. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

Rs 1800

 19

A trust fund has Rs. 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. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

Rs. 2000