1.3 Introduction to Matrices - Problems

1. 1. Form a 4 by 5 matrix, B, such that b_ij = i*j, where * represents multiplication.
      

   2. What is B^T?
      

   3. Is B symmetric? Why or why not?
      

2. Using matrix A below, spell words by replacing each element requested with the letter in that position of the matrix. For example, a₅₂a₂₁a₃₂ represents cat.
   
   
   
   
   1. a₅₃a₂₁a₃₂a₂₄a₁₄a₅₂a₁₂a₄₃          a₂₁a₂₄a₁₂           a₁₂a₂₁a₄₃a₃₃
      

   2. a₃₄a₂₄a₁₄a₁₂a₃₅a₅₅a₄₃
      

   3. a₅₂a₂₁a₁₃a₅₂a₄₄a₁₃a₂₁a₃₂a₄₁a₂₄
      

   4. Make up a statement of your own using the information given in this matrix. Write the statement using matrix elements and translate it. You have every letter of the alphabet in the matrix except the letter q.
   
   

3. 1. Put the following information into a 3 by 2 matrix and attach labels: The Lions won 5 games and lost 8. The Tigers won 9 and lost 4. The Bears won 7 and lost 6.
      

   2. Transpose the matrix from part (a) and attach labels.
      

4. 1. Each team played 15 games. They either won, lost, or tied each game. Put the following information into a 3 by 4 matrix and attach labels: The Snakes won 6 and lost 8. The Lizards won 8 and lost 7. The Frogs won 9 and tied 2. The Toads lost 9 and tied 1.
      

   2. Transpose the matrix from part (a) and attach labels.
      

   
   

5. 1. Put the following information into a 5 by 3 matrix and attach labels: Amit has a 3.48 GPA and scored 160 on his PSAT. His SAT score is 1580. Perry scored 121 on his PSAT and 1320 on the SAT. He has a 3.65 GPA. Don's GPA is 2.76, his SAT score is 840, and his PSAT score is 102. Heather scored 1260 on her SAT and 99 on the PSAT. She maintains a 3.80 GPA. Shelly scored 980 on the SAT and 83 on the PSAT with a GPA of 3.01.
      

   2. Transpose the matrix from part (a) and attach labels.
      

Computer Project

Write a computer program that will form a matrix from the numbers that the user enters. Make sure you specify how the user is to enter the information. You need to ask questions about the dimensions. Display the matrix and its transpose. Make this and all future programs user-friendly. Some high-level programming languages contain commands that will directly read, write, or manipulate a matrix for you. Do not use any of these commands. However, you will need to use arrays. Include comments in your code to tell your teacher (and yourself later) what you did.