Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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part e.

3. Each of J, K, L, M and N is a linear transformation from R to R', These functions are given as follows: J(11, 12) = (5x1 – 3z2, –10x1 + 672), K(x1, I2) = (-12, 1,), L(I1, 72) = (2, 1), M(I1,12) = (311 + I2, I1 + 2r2), N(r,, 12) = (-1,12). (a) In each case, write down the matrix of the transformation and compute its deter- minant. (b) Sketch a picture indicating what happens to the standard basis {(1,0), (0, 1)} un- der each function. (c) One of these functions is not injective. Which is it? (d) One of these functions is an anti-clockwise rotation of the plane. Which is it? (e) One of these functions is a reflection over the vertical axis. Which is it?
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Transcribed Image Text:3. Each of J, K, L, M and N is a linear transformation from R to R', These functions are given as follows: J(11, 12) = (5x1 – 3z2, –10x1 + 672), K(x1, I2) = (-12, 1,), L(I1, 72) = (2, 1), M(I1,12) = (311 + I2, I1 + 2r2), N(r,, 12) = (-1,12). (a) In each case, write down the matrix of the transformation and compute its deter- minant. (b) Sketch a picture indicating what happens to the standard basis {(1,0), (0, 1)} un- der each function. (c) One of these functions is not injective. Which is it? (d) One of these functions is an anti-clockwise rotation of the plane. Which is it? (e) One of these functions is a reflection over the vertical axis. Which is it?
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