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(g) .
(h) The range of is .
(i) is one-to-one.
Exercise Set 4.3
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By inspection, determine whether the linear operator is one-to-one.
1.
(a) the orthogonal projection on the x-axis in
(b) the reflection about the y-axis in
(c) the reflection about the line in
(d) a contraction with factor in
(e) a rotation about the z-axis in
(f) a reflection about the -plane in
(g) a dilation with factor in
Find the standard matrix for the linear operator defined by the equations, and use Theorem 4.3.4 to determine whether the
2. operator is one-to-one.
(a)
(b)
