1.7 Matrices (I)

• Types of matrices: column, row, square, rectangular, null and identity
• Properties of a matrix: elements, order, and compatibility of two or more matrices
• Addition and subtraction of compatible matrices; multiplication by a scalar and by a matrix
• Determinant and inverse of a 2 by 2 matrix; singular matrices
• Solving linear equations in two unknowns by the matrix method

• identify types of matrices using rows and columns
• determine properties of a matrix from rows and columns
• perform addition and subtraction of compatible matrices
• multiply compatible matrices in different situations
• compute the determinant of a 2 by 2 matrix
• determine the inverse of a 2 by 2 matrix
• solve linear equations in two unknowns using matrix method
• explore the use of matrices in real life situations

“How is the knowledge of matrices used in real life?”

The titles are open to everyone. Reading a lesson needs an account — sign in or create one.

1. Column, row, square and rectangular
   40 min · 1 practice tasks · quiz
   Name a matrix from its order: column, row, square or rectangular, and read an element by its row and column.
2. The null matrix and the identity
   40 min · 1 practice tasks · quiz
   Recognise a null matrix of a stated order, and the identity matrix of a square order.
3. Add and subtract compatible matrices
   40 min · 1 practice tasks · quiz
   Add three matrices of the same order, subtract in a stated order, and refuse a pair whose orders differ.
4. Multiply by a scalar
   40 min · 1 practice tasks · quiz
   Multiply every element by the same number, including a negative number, and combine that with subtraction.
5. When two matrices can be multiplied
   40 min · 1 practice tasks · quiz
   Multiply two matrices only when the columns of the first match the rows of the second, and read the order of the product from the outer numbers.
6. Multiply two square matrices
   40 min · 1 practice tasks · quiz
   Multiply two 2 by 2 matrices by pairing each row of the first with each column of the second.
7. A column or a row in the product
   40 min · 1 practice tasks · quiz
   Multiply a 2 by 3 matrix by a 3 by 1 column, and a 1 by 3 row by a 3 by 2 matrix.
8. The order of multiplication matters
   40 min · 1 practice tasks · quiz
   Show that AB and BA need not be equal, and that one of them may not even have the same order.
9. Multiply by the identity or the null
   40 min · 1 practice tasks · quiz
   Show that the 2 by 2 identity leaves a 2 by 2 matrix unchanged on either side, and that the null matrix produces the null product.
10. The determinant of a 2 by 2 matrix
    40 min · 1 practice tasks · quiz
    Compute the determinant of a 2 by 2 matrix as ad - bc, including a negative result.
11. A singular matrix
    40 min · 1 practice tasks · quiz
    Recognise a singular 2 by 2 matrix by a determinant of 0, including a singular matrix that is not the null matrix.
12. The inverse when the determinant is 1
    40 min · 1 practice tasks · quiz
    Build the inverse of a 2 by 2 matrix with determinant 1, and check it by multiplying back to the identity.
13. Divide by the determinant, or stop
    40 min · 1 practice tasks · quiz
    Find an inverse when the determinant is not 1, and refuse an inverse when the determinant is 0.
14. Two equations by the inverse
    40 min · 1 practice tasks · quiz
    Write two linear equations as a matrix times a column, then multiply by the inverse to find the unique solution.
15. No unique solution
    40 min · 1 practice tasks · quiz
    When the coefficient matrix is singular, stop the inverse method and decide whether the equations have many solutions or none.
16. Prices from two purchases
    40 min · 1 practice tasks · quiz
    Turn two classroom purchases into a matrix equation, find the two prices when they are unique, and stop when the purchases are multiples.