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balu736 [363]
3 years ago
8

Suppose A is an m × n matrix in which m> n. Suppose also that the rank of A equals n Show that A is one to one. Hint: If not,

there exists a vector x such that Ax = 0, and this implies at least one column of A is a linear combination of the others. Show this would require the rank to be less than n.
Mathematics
1 answer:
rusak2 [61]3 years ago
7 0

Step-by-step explanation:

If T:Rn→Rm is a linear transformation and if A is the standard matrix of T, then the following are equivalent:

 1.  T is one-to-one.

 2. T(x) = 0 has only the trivial solution x=0.

 3.  If A is the standard matrix of T, then the columns of A are linearly independent.

Here, A is a mxn matrix where m ≥ n and the rank of A equals n. It implies that the columns of A are linearly independent, for, otherwise, the rank of A would be less than n. Hence the linear transformation represented by A is one-to-one.

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Look at pic 10 pts will mark brainilest
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Answer:

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6 0
2 years ago
Find the number of pairs (a,b) of integers such that<br> a+2/a+5=b/3
Viktor [21]

Answer:

  6

Step-by-step explanation:

The expression can be rearranged to ...

  b = 3 -9/(a+5)

In order for b to be an integer, (a+5) must be an integer divisor of 9. There are exactly 6 of those: ±1, ±3, ±9.

The attached table shows the values (a, b) = (x₁, f(x₁)).

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3 years ago
Solve 2x2 + 4x +10 = 0 using the quadratic formula. what is the solution set?
Sergio [31]
/If you solve for x you will get -7/2.
5 0
3 years ago
X squared -8x+14=2x-7
Stella [2.4K]

Answer:

x = 3 or x = 7

Step-by-step explanation:

X² - 8x + 14 = 2x - 7

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Now we have a quadratic equation ;

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2 years ago
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Answer:

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Step-by-step explanation:

you set up a equation that looks like this

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___     =      ______

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you mutiply 100 by 86 and get 8600 then you divide that by 150 and get 57.333333333 as your finally answer.

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3 years ago
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