1. (10 points) Indicate whether each of the following is true or false. If false, please explain why it is false. (a) It is possible for a system of linear equations to have exactly two solutions. (b) A 3x7 matrix is a matrix with 3 columns and 7 rows. (c) If there is a row in an augmented matrix of the form 0000...16, then the system has no solution. 1 2 2 -4 (d) IfM= ] then - 2M 3 4 -6 -8 (e) The rate of change of j with respect to k is given by change in change in j 2. (10 points) Solve the following system of linear equations using an augmented matrix. 62 +2.29 - 4.13 = 4 * - 2.72 +233 8.21 4.r2 - 12.13 = 12 3. (15 points) Micah wants to use eggs and tofu to increase the amount of protein and selenium in his diet. According to his calculations, he needs 54 grams of protein and 36 micrograms of selenium from these sources. An egg contains 6 grams of protein and 15 micrograms of selenium. A serving of peanut butter contains 8 grams of protein and 2 micrograms of selenium. Write the system of equations that represents this scenario as well as the corresponding augmented matrix. Then, use the matrix to find the number of eggs and servings of peanut butter Micah needs to consume to get exactly the 54 grams of protein and 36 micrograms of selenium he wants. 4. (5 points Draw the pranh for > 4 Make sure to lahal wave 4. (5 points) Draw the graph for y3x + 4. Make sure to label your axes. 5. Suppose you are given the following linear model relating the market price (p, in dollars) of face masks to their demand (d, in hundreds of thousands): p = 0.150 +5. (a) Interpret the slope of the model. (b) Use the model to estimate the demand when cloth face masks have a market price of $8.60. (c) Use the model to estimate the market price (to the nearest whole cent) of cloth face masks when demand is 1,540,000. 1. (10 points) Indicate whether each of the following is true or false. If false, please explain why it is false. (a) It is possible for a system of linear equations to have exactly two solutions. (b) A 3x7 matrix is a matrix with 3 columns and 7 rows. (c) If there is a row in an augmented matrix of the form 0000...16, then the system has no solution. 1 2 2 -4 (d) IfM= ] then - 2M 3 4 -6 -8 (e) The rate of change of j with respect to k is given by change in change in j 2. (10 points) Solve the following system of linear equations using an augmented matrix. 62 +2.29 - 4.13 = 4 * - 2.72 +233 8.21 4.r2 - 12.13 = 12 3. (15 points) Micah wants to use eggs and tofu to increase the amount of protein and selenium in his diet. According to his calculations, he needs 54 grams of protein and 36 micrograms of selenium from these sources. An egg contains 6 grams of protein and 15 micrograms of selenium. A serving of peanut butter contains 8 grams of protein and 2 micrograms of selenium. Write the system of equations that represents this scenario as well as the corresponding augmented matrix. Then, use the matrix to find the number of eggs and servings of peanut butter Micah needs to consume to get exactly the 54 grams of protein and 36 micrograms of selenium he wants. 4. (5 points Draw the pranh for > 4 Make sure to lahal wave 4. (5 points) Draw the graph for y3x + 4. Make sure to label your axes. 5. Suppose you are given the following linear model relating the market price (p, in dollars) of face masks to their demand (d, in hundreds of thousands): p = 0.150 +5. (a) Interpret the slope of the model. (b) Use the model to estimate the demand when cloth face masks have a market price of $8.60. (c) Use the model to estimate the market price (to the nearest whole cent) of cloth face masks when demand is 1,540,000