Read the summary and the most important questions on Math Tutor DVD - Matrix Algebra

• 1 Introduction to Matrices

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• In the context of a systems of equations, how does the amount of unknown variables relate to the number of equations you need to solve for those unknowns? (in other words: if you have 3 unknowns how many equations would you need?)

  The numbers are always equal; solving for 2 unknown variables requires 2 equations, 3 unknown variables requires 3.

• What is meant with the 'order of a matrix'? and how would we answer the question: What is the order of a particular matrix?

  The order of a matrix relates the number of rows and columns. So if it has 2 rows and 3 columns, you would answer the question by saying that the matrix has a order of 2 by 3.

• What is an element of a matrix?

  An element is a specific number inside the matrix, if it has 6 numbers it has 6 elements.

• Matrix 1        Matrix 2[ 1  2 ]             [  1   2  3 ][ 3 4 ]             [ 4  5  6 ][ 5 6 ]  Are the above 2 matrices equal to each other?

  No they are not, even though they have the exact same elements inside, they dont have the same order (aka size and shape aka rows and columns): 1 has 3 rows and 2 columns and number 2 has 2 rows and 3 columns.

• 2 Add, Subtract Matrices and Multiply by a Scalar

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• Can you add or subtract matrices that dont have the same order?

  No you cannot.

• Explain the following notation:A + B = [a sub i, sub j, + b sub i, sub j ]  (see image)

  This means that A and B are both matrices and what it means to add them together: the corresponding value for an element in matrix A added to the corresponding value for an element in matrix B) this is the same for subtraction as well.

• Explain very shortly what it means to add 2 matrices together.

  Go to each element in the first matrix, go to each corresponding element in second matrix and add them together. 
  
  Matrix A:
  [ 2 3 4 ]
  [ 3 5 6 ]
  
  Matrix B:
  [ 1 3 3 ]
  [ 2 4 6 ]
  
  A + B = 
  [ 3 6 7 ]
  [ 5 9 12 ]
  
  See how the Row 1 Col 1 of Matrix A is added to Row 1 Col 1 from Matrix B?

• Does the subtracting matrices work the same as adding them?

  Yes

• 3 Multiplying Matrices Together

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• What is the only way (the main requirement) you can multiply 2 matrices together?

  The only way you ca multiply 2 matrices together is when the the number of columns of the first matrix is equal to the number of rows (yes rows) of the 2nd matrix.

• In the context of multiplying matrices, what would happen if the first matrix had 2 rows and 2 columns and the second matrix had 3 rows and 4 columns?

  The number of columns of the first matrix should be equal to the number of rows of the second matrix. This not the case here, (Matrix #One has 2 columns, Matrix #Two has 3 rows), therefore multiplication can't be done.