5. Compute [2 1 3 3] [ 3 4 4 2]in Z^4 sub 5.
6. Find a system of two linear equations in the variables x and y whose solution set is given by the
parametric equations x = t and y = 3 – 2t.
7. Find another parametric equation to the system in item 6 in which the parameter is s and y =s.
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5. To compute [2 1 3 3] [ 3 4 4 2] in Z^4 sub 5, we perform matrix multiplication:
[2 1 3 3] [ 3 4 4 2] = (2*3 + 1*4 + 3*4 + 3*2) modulo 5
= (6 + 4 + 12 + 6) modulo 5
= 28 modulo 5
= 3 modulo 5
= 3
So the result is 3.
6. To find a system of two linear equations given the parametric equations x = t and y = 3 – 2t, we can equate the variables in each equation and solve for the coefficients:
x = t
y = 3 - 2t
Rewriting the equations:
1x + 0y = 1t
0x + 1y = 3 - 2t
This gives the system of linear equations:
x = t
y = 3 - 2t
7. To find another parametric equation to the system in item 6 where the parameter is s and y = s, we can substitute s for y in the original parametric equations:
x = t
s = 3 - 2t
This gives the new parametric equation: x = t, y = 3 - 2x.
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