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# IB Maths SL Matrices

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### IB Maths SL Matrices

1. 1. A matrix is an ordered set of numbers listed in rectangular form Matrix A has 2 rows and 3 columns. We say it is a 2x3 matrix. order 2x3
2. 2. B is a row matrix. C is a column matrix. This is the 3x3 zero-matrix. I is the 3x3 Identity matrix. and are opposite matrices.
3. 3. We can sum matrices of the same order. Multiplication of a matrix by a scalar =3
4. 4. To multiply matrices, we multiply rows into columns: 2 x 3 3x 2 = 2x 2 = What special name has the answer?
5. 5. Determinant of a matrix Determinant of a matrix is a number calculated from the elements of the matrix. A = det A=
6. 6. Determinant of a 3x3 matrix
7. 7. Find the determinant of:
8. 8. If P= , find the value of x for which |P| = 0. If the determinant of a matrix is zero ,  the matrix is called a singular matrix
9. 9. Inverse of a matrix Only square matrices have inverses. Not all square matrices have inverses. matrix A has an inverse A­1         |A| ≠ 0 singular matrices have no inverse
10. 10. 2x2 matrices: or using GDC: x-1 key 3x3 matrices: using GDC: x-1 key
11. 11. Solutions of systems of linear equations Using matrices we can rewrite these equations as: A X = B A­1 (AX) = A­1 B (A­1  A) X  = A­1 B I   X  = A­1 B    X  = A­1 B
12. 12.    X  = A­1 BA       X  =  B ⇒ X ⇒ x = 3  , y = 1
13. 13. Given the simultaneous equations: write them in matrix form and find x, y and z.
14. 14. using GDC :
15. 15. Use your GDC to find the inverse of the matrix Hence, solve the simultaneous equations: 4 11 5 1 4 2 1 2 1 4 x + 11 y + 5 z = 2     x + 4  y + 2 z =  1    x + 2  y + 1  z =  4
16. 16. The matrix A = 2 0 2 5 1 0 ­1 4 a a) Find an expression in terms of a for detA. b) Find the value of a for which A-1 does not exist. c) Solve the equation A when a = 0 giving your answers correct to 3 s.f.
17. 17. Exercise Book page 336 Ex 1 a), 2 and 5 page 337 : EX8, 10, revision exercise 12 page 339