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Matrices | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

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  • How to show the matrix
    • A matrix has row and columns
    • Rows are the horizontal ones
    • Columns are the vertical ones
    • We write the matrix equation in the form of row x column
    • So a matrix with 3 rows and 4 columns can be written as 3 x 4
    • Matrices are always named with capital letters.
  • Unity Matrix
    • This matrix is called unity because when we multiply this matrix with anything, it brings no change in its value.
  • Addition and Subtraction of Matrices
    • Matrices with the same formation can be added or subtracted
    • In other words, rows and columns of both matrices should be the same.
    • The addition and subtraction is simple, if the two matrices are as follows:
    • +

    • Then we will add a and e, f and b, c and g, and h and d.
  • Multiplication and division of matrices
    • Check the video for the details on how to do the multiplication and division. However, a few important rules are as follows.
    • Direct division of matrices is not possible.
    • For multiplication, we can only multiply two matrices where the column number of the first matrix is equal to the row number of the second matrix.
      • The new matrix that will be created will have the row number of the first matrix and the column number of the second matrix.
      • Therefore, 3×4 and 4×5 can multiply together because the column number of the first matrix and the row number of the second matrix are equal.
        • The final matrix will  have 3 rows and 5 columns
    • It must be noted that for the two same matrices, say A and B, A x B is not the same as B x A. In some cases, one may be possible, the other may not be.
      • For example, if A is 3 x 4 and B is 4 x 5, then A x B is possible.
      • However, B x A is not possible because of the rule mentioned above.
  • Division of Matrices
  • To divide matrices, we use inverses. For example, if we need A/B, then what we can do is A x B^-1
        • We can write B^-1 or B’
    • Inverse Process
      • First, we take the determinant
      • For a matrix
      • The determinant |B| = a*d – (b*c)
        • If the answer is zero, we say that no inverse is possible.
      • Then, we find Adjacent of the of the matrix
        • Adj B =
      • Now the inverse process, is as follows
      • (1/det B) x Adj B
  • Another use of transformation
    • In transformation, if the Matrix A maps an object to Image, then multiplying the Image with A inverse will map it back into the object.
  • How to multiply
    • Use the video to determine how the multiplication process is done.
  • For algebra.
    • AB=C
    • Then we can take B or A on the other side of the equation in the form of inverse
    • A = Cx(B Inverse)
    • OR
    • B= (A Inverse) x C
    • Remember, the place of the matrix on the same side of the other end of the equation as it was originally. If it was placed first, place it’s inverse first. If it was placed second, place it’s inverse second.
Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

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