Need Linear Algebra Questions 62-65 True or False? In Exercises 62-65, determine
ID: 3146430 • Letter: N
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Need Linear Algebra Questions 62-65
True or False? In Exercises 62-65, determine whether each state- ment is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 62, (a) The nullspace of A is also called the solution space of A. (b) The nullspace of A is the solution space of the homogeneous system Ax = 0. 63.) (a) If an m x n matrix A is row-equivalent to an mx n matrix B, then the row space of A is equivalent to the row space (b) If A is an m x n matrix of rank r, then the dimension of the 64./ (a) If an m x n matrix B can be obtained from elementary row of B solution space of Ax = 0 is m-r operations on an m × n matrix A, then the column space of B is equal to the column space of (b) The system of linear equations Ax = b is inconsistent if and only if b is in the column space o 65. (a) The column space of a matrix A is equal to the row space of A (b) Row operations on a matrix A may change the dependency relationships among the columns of A.Explanation / Answer
62.
(a)False ,
The nullspace of A is also called the solution space of the system Ax=0
(b)True
The nullspace of A is the solution space of homogeous system Ax=0
63.
(a) true
Two matrices ,m×n are row equivalent if and only if they have the same row space
(b)False
The rank of a matrix is number of column(row) pivots, it must be less than equal to m and n.
64.
(a)True
The elementary row operations do not change the row space of a matrix. However it does not change the column space of matrix.
(b)True
65.
(a)True
Transpose matrix of A (AT) exchange the row with column of matrix A.
(B) True
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