5. Can a matrix that has 0 entries for an entire row have one solution? Explain why or why not. Algebraic For the following exercises, write the augmented matrix for the linear system. Q x+5y+32=19 _'12x+3y=4 3x+4y+92=7 6x+12y+162=4 ILA-lad \f\f\f\fExtensions For the following exercises, use Gaussian elimination to solve the system. T 3 4 4?. x = Real-World Applications For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. -52. Every day, a cupcake store sells 5,000 cupcakes in chocolate and vanilla flavors. If the chocolate flavor is @ times as popular as the vanilla flavor, how many of each cupcake sell per day? 53. At a competing cupcake store, $4,520 worth of cupcakes are sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost $1.75. If the total number of cupcakes sold per day is 2,200, how many of each flavor are sold each day? 54. You invested $ 10,000 into two accounts. one that has simple 3% interest, the other with 2 5% interest If your total interest payment after one year was $285.50, how much was in each seeount after the year passed? 55. You invested $2,300 into account 1, and $2,700 into account 2. If the total amount of interest after one year is $254-and account 2 has 1 5 times the interest rate of account 1, what are the interest rates? Assume simple interest rates.. 56 Bikes'B'I Is manufactures bikes, which sell for $250.It costs the manufacturer $180 per bike, plus a startup- fee of $3,500. After how many bikes cold will the manufacturer break even? 57. A major appliance store is considering purchasing vacuums from a small manufacturer. The store would be able to purchase the vacuums for $86 each, with a delivery fee of $9,200, regardless of how many vacuums are sold. If the store needs to start seeing a profit after 230 units are sold, how much should they charge for the vacuums?61. A bag of mixed nuts contains cashews, pistachios, and almonds. Originally there were 900 nuts in the bag. 30% of the almonds, 20% of the cashews, and 10% of the pistachios were eaten, and now there are 770 nuts left in the bag. Originally, there were 100 more cashews than almonds. Figure out how many of each type of nut was in the bag to begin with