![Mathematics](/tpl/images/cats/mat.png)
Mathematics, 21.05.2020 19:58, tumadreeve7852
Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In.
A. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In
B. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nxn identity matrix, In.
C. Suppose A is n x n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In.
![answer](/tpl/images/cats/otvet.png)
Answers: 1
Other questions on the subject: Mathematics
![image](/tpl/images/cats/mat.png)
Mathematics, 21.06.2019 19:30, tgentryb60
Now max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.
Answers: 1
![image](/tpl/images/cats/mat.png)
![image](/tpl/images/cats/mat.png)
Mathematics, 22.06.2019 00:30, starfox5454
How many square centimeters of wrapping paper will be used to wrap the shoe box?
Answers: 1
![image](/tpl/images/cats/mat.png)
Mathematics, 22.06.2019 01:50, ElegantEmerald
If f (x) = 2x2 +5/(x-2), complete the following statement: f(6) =
Answers: 3
Do you know the correct answer?
Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot...
Questions in other subjects:
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/himiya.png)
Chemistry, 24.03.2021 20:30
![Konu](/tpl/images/cats/fr.png)
French, 24.03.2021 20:30
![Konu](/tpl/images/cats/ekonomika.png)
![Konu](/tpl/images/cats/mat.png)
Mathematics, 24.03.2021 20:30
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/mat.png)
![Konu](/tpl/images/cats/mat.png)