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Matrices - solving two simultaneous equations

and. B = ( 4. 1 we have. AX = B. This is the matrix form of the simultaneous equations. Here the only unknown is the matrix X.



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Consider a system of two simultaneous linear equations: Multiply Equation (1) by and Equation (2) by : Subtract Equation (4) from Equation (3). Making 



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CHAPTER 4 Systems of Linear Equations; Matrices. SOLUTION Solve either equation for one variable in terms of the other; then.



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Year 12 fm = Matrices (Sim. linear equations) = Worksheet 1. 1. Use inverse matrix method to solve the following system of simultaneous linear equations.



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[PDF] year-12-matrices-worksheet-1pdf - itutecom

1 Use inverse matrix method to solve the following system of simultaneous linear equations 1 3 7 3



[PDF] SOLVING SIMULTANEOUS EQUATIONS USING MATRICES

When the coefficient matrix A is singular it means that the system of simultaneous equations has NO UNIQUE SOLUTION There are two possible cases: det(A) = 0

  • How do you solve simultaneous equations with matrices?

    Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.

  • How to solve simultaneous equations

    1Use the elimination method to get rid of one of the variables.2Find the value of one variable.3Find the value of the remaining variables using substitution.4Clearly state the final answer.5Check your answer by substituting both values into either of the original equations.

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= Year 12 fm = Matrices (Sim. linear equations) = Worksheet 1

1. Use inverse matrix method to solve the following system of

simultaneous linear equations. 1373
yxyx

2. Use inverse matrix method to solve the following system of

simultaneous linear equations. 21
43
521
32
yxxy

3. Use CAS/calculator to solve for x and y.

-9.71.5

7.29.33.173.0

yx

4. Use CAS/calculator to solve for a, p and t.

2152103

4 3 54
6521
32
4321
72
51tpa

5. Use CAS/calculator to solve the following system of

simultaneous linear equations.

3455.1222.0132

yzxwxyzywzx

6. A system of simultaneous linear equations can be

represented by the following matrix equation. -41 32
yx baba. The solutions to the equations are 2=x and

1-=y. Find the values of a and b, and state the

simultaneous equations.

7. Write the system of simultaneous equations in matrix form.

57352753

byaxbyax

Find a and b when 3

==yx.

8. Consider the simultaneous equations in Q7.

57352753

byaxbyax

Use matrix method to find a and b when

ax= and by=.

9. Write the system of simultaneous equations in matrix form.

14339221152

rzqypxrzqypxrzqypx

Find p, q and r when

1=x, 1-=y and 2=z.

Numerical, algebraic and worded answers.

1. x = 1, y = -2

2. x = -10/9, y = 34/27

3. x = 3.4143, y = 2.0058

4. a = 0.9915, p = -0.4676, t = -0.0638

5. w = 2.5171, x = -0.2051, y = -0.6111, z = -0.4701

6. a = ½, b = 1, x + y = 1, ½ x - 3y = 4

7. 5727
3553
yx baba , a = 2, b = 3

8. a = ±⎷6, b = ±3

9. 14 911

332252

z yx rqprqprqp , p = -1, q = 3, r =1quotesdbs_dbs14.pdfusesText_20
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