Posted at 9:19 pm by Miss Loi in A-Maths Notes & Tips
木
曜
日
2008
Thu
1
May
Miss Loi avatar

Of Matrices & Miss Loi’s Day Of Labour

(10)
Miss Loi's 2008 Day of Labour Route
This year’s Great Labour Day Racing Circuit
certainly looks tame compared to last year’s

*Takes off helmet*

*Shows kindly & benign face*

On a day when Singapore’s working class was left to reflect on their social standing in the current status quo, May 1st (by virtue of its proximity to the Mids) has traditionally been Miss Loi’s Day of Labour.

But with the advent of The Temple, the distance travelled is much less this year, with a corresponding drop in the number of stunts overtaking manoevuers needed in order to get to her students’ place on time.

Which also means that Miss Loi actually has time to help that butchy Sergeant Loi (who is on leave today and thereby sparing the serene Temple Grounds from her KPKB for the first time this week) post her Matrices notes:

Ever since the bulk of the Matrices chapter has been migrated over to the New EMaths Syllabus, according to Section 1.4 of the AMaths Syllabus, about the only time you’ll ever see matrices appearing in your AMaths papers would be when you’re asked to solve a pair of simultaneous equations using the inverse matrix method.

The following, then, is really all you need to know :)

Solving Simultaneous Equations Via Inverse Matrix

A. HOW TO MULTIPLY MATRICES

Multiplication of Matrices

B. DETERMINANT OF A 2X2 MATRIX

Determinant of matrix M = ({matrix{2}{2}{a b c d}}) is given by:
|M| = delim{|}{matrix{2}{2}{a b c d}}{|} = ad - bc

If |M| = 0 ⇒ M is singular.
If |M| ≠ 0 ⇒ M is non-singular.

C. INVERSE OF A 2X2 MATRIX

For a non-singular matrix M = ({matrix{2}{2}{a b c d}}),
Inverse Matrix

D. THE INVERSE MATRIX METHOD

AX = B ⇒ X = A-1B

*Note: AX = B ⇏ X = BA-1!

SAMPLE PRACTICE QUESTION

Use the inverse matrix method to solve the simultaneous equations:

5x + y = -8
-x + 2y = 17

Ans:

*See the words inverse matrix method in question - SIANZ!*

  1. Can you see that the pair of simultaneous equations are actually part of matrix multiplications shown in A above? So you can convert to matrix form:
    (matrix{2}{2}{5 1 {-1} 2})(matrix{2}{1}{x y}) = (matrix{2}{1}{{-8} 17})

    You can then move the 4 x4 matrix to the RHS of the equation as highlighted in D above:
    doubleright (matrix{2}{1}{x y}) = (matrix{2}{2}{5 1 {-1} 2})^-1(matrix{2}{1}{{-8} 17})

  2. Now to find the inverse matrix (matrix{2}{2}{5 1 {-1} 2})^-1:

    As described in B above:
    Determinant → delim{|}{matrix{2}{2}{5 1 {-1} 2}}{|} = (5)(2)-(1)(-1) = 11 ≠ 0
    ⇒ non-singular
    ⇒ inverse exists!

    As described in C above:
    So (matrix{2}{2}{5 1 {-1} 2})^-1 = {1/11}(matrix{2}{2}{2 {-1} 1 5})

  3. Sub the inverse into the equation in step i:
    (matrix{2}{1}{x y}) = {1/11}(matrix{2}{2}{2 {-1} 1 5})(matrix{2}{1}{{-8} 17})

    Do your multiplication! As described in A above:
    (matrix{2}{1}{x y}) = {1/11}(matrix{2}{1}{{(2)(-8)+(-1)(17)} {(1)(-8)+(5)(17)}})
    doubleright (matrix{2}{1}{x y}) = {1/11}(matrix{2}{1}{{-33} 77}) = (matrix{2}{1}{{-3} 7})
    ⇒ x = -3, y = -7

    Note: most of the time, you should end up with a 2 x 1 matrix after multiplying.

Know with true faith the methods above. Be cautious with the pointers and common mistakes in red. Understand with thy heart the representative sample question at hand.

Print this out if necessary and commit to memory the above procedures, and be comforted that no matter what happens, Miss Loi shall always be here to support you, in spirit and in soul.

HAPPY LABOUR DAY!

*Drifts away like 倩女幽魂*

がんばって!!!
Miss Loi
,

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Comments

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10 Comments

  1. 1
    木
    曜
    日
    2008
    Thu
    1
    May
    9:24PM
    ignorantsoup says,

    Happy Labour day Sergeant Miss Loi.

  2. 2
    木
    曜
    日
    2008
    Thu
    1
    May
    11:16PM
    Miss Loi avatar Miss Loi says,

    Happy Labour Day to you too Soupie!

    All of you better be good har … coz holiday’s ending and Sergeant Loi’s coming back from her leave.

    *Hears distant sound of cracking whip*

  3. 3
    金
    曜
    日
    2008
    Fri
    2
    May
    11:29AM
    |c3^sNoW says,

    WAH n in my time matrices was removed from all my maths syllabus from O to A levels. tsktsk. poor kids.

  4. 4
    金
    曜
    日
    2008
    Fri
    2
    May
    12:21PM
    Miss Loi avatar Miss Loi says,

    |c3^sNoW-chan, matrices should be far, far, far removed from your mind since you should be enjoying your Golden Week now.

    Tsk. tsk. Poor Miss Loi later still got class :(

  5. 5
    金
    曜
    日
    2008
    Fri
    2
    May
    2:49PM
    |c3^sNoW says,

    ryn: no Miss Loi, i dunno coz nv ask my parents 2 send me money…u gt japanese account ah!
    n no lor, i still have to go lab tomorrow…when everyone is frolicking away in the nice spring sun. :(

  6. 6
    金
    曜
    日
    2008
    Fri
    2
    May
    2:50PM
    |c3^sNoW says,

    oh Miss Loi gambatte!
    or shld i say, Sergeant Loi? :p

  7. 7
    土
    曜
    日
    2008
    Sat
    3
    May
    12:17AM
    Miss Loi avatar Miss Loi says,

    |c3^sNoW-chan: Please treasure and cherish your nice spring sun - especially when all we have here these days are either stifling heatwaves or flood-inducing freak showers :(

  8. 8
    土
    曜
    日
    2008
    Sat
    3
    May
    12:23PM
    |c3^sNoW says,

    JR is my initials :p i own e JR rail u noe :p n yup, i work in a lab but im not harry potter :D or hermione granger :p

  9. 9
    土
    曜
    日
    2008
    Sat
    3
    May
    7:01PM
    vivien says,

    hihi..would you be able to upload notes on quardratic equation which includes modulus function and roots? my exam is on tues..6 may

  10. 10
    日
    曜
    日
    2008
    Sun
    4
    May
    12:57AM
    Miss Loi avatar Miss Loi says,

    Hi Vivien, Miss Loi will try … but meanwhile do check out the past quadratic questions here if you haven’t yet done so ;)

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