1 Tutorial Questions
(a) Let C=
311
151
113
. What is the dimension of the product B= (x, y, z)·C·
x
y
z
?
Calculate B. Find |C|and, using Gauss Jordan elimination, find the inverse of C.
(b) Find the inverse of the matrix A=
310
−2−4 3
5 4 −2
.
(c) Use elementary row operations to find A−1if A=
124
202
113
and A=
100
204
517
.
(d) Use row operations to determine the inverse of A=
1 1 1 1
1 2 −1 2
1−121
1 3 3 2
.
(e) Let W=
121 a
251 a
−1 1 −3−3a+ 1
3 8 1 2a
. Find all values of afor which the matrix Whas
an inverse and calculate the inverse of Wfor one such value of a.
(f) Solve the following systems
(a)
2x+y−2z= 10
3x+ 2y+ 2z= 1
5x+ 4y+ 3z= 4
(b)
x+ 2y−3z= 6
2x−y+ 4z= 2
4x+ 3y−2z= 14
(c)
x+ 2y+ 2z= 2
3x−2y−z= 5
2x−5y+ 3z=−4
x+ 4y+ 6z= 0
(d)
x+ 5y+ 4z−13w= 3
3x−y+ 2z+ 5w= 2
2x+ 2y+ 3z−4w= 1
.
(g) Suppose that the following matrix Ais the augmented matrix for a system of linear
equations.
A=
ccc|c1 2 3 4
2−1−2a2
−1−7−11 a
where ais a real number. Determine all the values of aso that the corresponding
system is consistent.
(h) Find the rank of the following real matrix
a1 2
1 1 1
−111−a
where ais a real number.
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