1MA01: Mathematical Methods Tutorial Sheet 3
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1. Write down the 3 × 3 identity matrix, denoted I.
Given the 3 × 3 matrix,


1 2 5


A =  6 0 1 ,
3 2 7
(1)
show, by calculation, that AI = IA = A.
2. Sketch the lines represented by the two equations below.
Solve for a and b, by writing in matrix form and using Gauss-Jordan
elimination, the following system of equations.
5a − b = 14
2a + 3b = 26
Check your answer is correct.
3. Use Gauss-Jordan elimination to solve the following equations for x, y, z.
x + y + 2z = 5
x + y + z = −10
2x + 3y + 4z = 2
Check your answer is correct.
4. Consider the system of equations
2x − y = −5
−2x + y = −2
Sketch the two lines represented by these equations. What do you
notice?
Can you solve for x and y using Gauss-Jordan elimination? What
happens?
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Sinéad Ryan, ryan@maths.tcd.ie, see also http://www.maths.tcd.ie/ ryan/123.html