Matrix: Additional questions set 1 1. John has inherited $25,000 and put the money in three types of investment a money market account, municipal bonds and a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutually fund paid 8% annually. His investment in the bonds is s6,000 more than that in the mutual funds. Find the amount John invested in each type of investment. (ay Write down the matrix equation (Ax b)representing the problem. (b) Use GaussJordan method to obtain the inverse of the matrix A in part (a) (c) Use the answer from (b to determine the amount of each type of investment. 15000 25000 ANS 0.06 0.07 0.08 x, 1620 x 8000 2000 L ,J l 6000 0 2 0 and C 2. Let A 0 2 5 a) Find det A and adjoint of A (adj A if (A (BT) -I b) Find B c) Solve A x -2 10 13 -2 33 -10 4 ANS. det A. 20, adj (Al)- 0 10 0 B1- 85 30 0 20 3. For a system of linear equation below where C and D are real constants x, 2x, x 5x, 2x 1 x 2x, 5x2 2x3 x 6 2-3x -6x x, 3x, Cx, 4x 5 Dx a) Write down the matrix equation (Ax b)and the augmented matrix that represents the above system of linear equations b) What are values of C and D that make this system inconsistent? Sasi thon Bland 1703/2016
Show transcribed image text Matrix: Additional questions set 1 1. John has inherited $25,000 and put the money in three types of investment a money market account, municipal bonds and a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutually fund paid 8% annually. His investment in the bonds is s6,000 more than that in the mutual funds. Find the amount John invested in each type of investment. (ay Write down the matrix equation (Ax b)representing the problem. (b) Use GaussJordan method to obtain the inverse of the matrix A in part (a) (c) Use the answer from (b to determine the amount of each type of investment. 15000 25000 ANS 0.06 0.07 0.08 x, 1620 x 8000 2000 L ,J l 6000 0 2 0 and C 2. Let A 0 2 5 a) Find det A and adjoint of A (adj A if (A (BT) -I b) Find B c) Solve A x -2 10 13 -2 33 -10 4 ANS. det A. 20, adj (Al)- 0 10 0 B1- 85 30 0 20 3. For a system of linear equation below where C and D are real constants x, 2x, x 5x, 2x 1 x 2x, 5x2 2x3 x 6 2-3x -6x x, 3x, Cx, 4x 5 Dx a) Write down the matrix equation (Ax b)and the augmented matrix that represents the above system of linear equations b) What are values of C and D that make this system inconsistent? Sasi thon Bland 1703/2016