Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Finding the Nullity and Describing the Kernel and Range In Exercises 33-40, let T: R³ R³ be a linear transformation. Find the nullity of T and give a geometric description of the kernel and range of T. 33. rank(7) = 2 = 1 35. rank(T) = 0 3 37. T is the counterclockwise rotation of 45° about the z-axis: T(x, y, z) = T(x, y, z) = 34. rank(T) 36. rank(T) /2 (1²2x - 1/², 1/² x + √² x ²) y, z) X y, 2 2 2 38. T is the reflection through the yz-coordinate plane: T(x, y, z)=(x, y, z) 39. T is the projection onto the vector v = (1, 2, 2): x + 2y + 2z 9 = (1, 2, 2) 40. T is the projection onto the xy-coordinate plane: T(x, y, z)=(x, y, 0)
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Transcribed Image Text:Finding the Nullity and Describing the Kernel and Range In Exercises 33-40, let T: R³ R³ be a linear transformation. Find the nullity of T and give a geometric description of the kernel and range of T. 33. rank(7) = 2 = 1 35. rank(T) = 0 3 37. T is the counterclockwise rotation of 45° about the z-axis: T(x, y, z) = T(x, y, z) = 34. rank(T) 36. rank(T) /2 (1²2x - 1/², 1/² x + √² x ²) y, z) X y, 2 2 2 38. T is the reflection through the yz-coordinate plane: T(x, y, z)=(x, y, z) 39. T is the projection onto the vector v = (1, 2, 2): x + 2y + 2z 9 = (1, 2, 2) 40. T is the projection onto the xy-coordinate plane: T(x, y, z)=(x, y, 0)
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