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Math 152 Homework 4
Linear Algebra (California State University Fresno)
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Math 152
Spring 2021
Name: Vouchnai Chheang
Homework 4- Due Wednesday
Exercise 2.5.8 In each case factor A as a product of elementary matrices.
Exercise 2.5.9 Let E be an elementary matrix.
a. Show that E T is also elementary of the same type
First, Multiplying a row by a non zero constant.
ET is same as the matrix E ( ET is elementary)
interchange of two rows, we get ET is same as the matrix E.
Thus, ETET is also elementary.
While, adding a non-zero multiple of one row to another, we have:
Rj+lRi=Rj, l≠0
So, with lone exception that:
Eji=l≠0
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Then, the transpose, we get
Eji=l
This is same as the elementary matrix obtained by the
operation:
lRj+Ri=Ri
Therefore, the matrix F=ET is also an elementary matrix.
Hence, it can be concluded that ET is also elementary of the
same type.
Exercise 2.6.1 Let T : R 3 → R 2 be a linear transformation.
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Exercise 2.6.3 In each case assume that the transformation T is linear, and use Theorem 2.6.2 to
obtain the matrix A of T.
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Exercise 2.7.3 In each case use the given LUdecomposition of A to solve the system Ax = b by
finding y such that Ly = b, and then x such that Ux = y:
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Exercise 2.9.4 Assume that there are three social classes—upper, middle, and lower—and that
social mobility behaves as follows:
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Exercise 3.1.1 Compute the determinants of the following matrices.
Exercise 3.1.2 Show that det A = 0 if A has a row or column consisting of zeros.
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Exercise 3.1.9 In each case either prove the statement or give an example showing that it is false:
Exercise 3.1.16 Find the real numbers x and y such that det A = 0 if:
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