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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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Im confused..I feel as if what I’m learning in class itself is not as difficult as the problems my teacher gives us to take home
RideAnS [48]
Ok, so remember that the derivitive of the position function is the velocty function and the derivitive of the velocity function is the accceleration function

x(t) is the positon function
so just take the derivitive of 3t/π +cos(t) twice
first derivitive is 3/π-sin(t)
2nd derivitive is -cos(t)
a(t)=-cos(t)

on the interval [π/2,5π/2) where does -cos(t)=1? or where does cos(t)=-1?
at t=π
so now plug that in for t in the position function to find the position at time t=π
x(π)=3(π)/π+cos(π)
x(π)=3-1
x(π)=2
so the position is 2







ok, that graph is the first derivitive of f(x)
the function f(x) is increaseing when the slope is positive
it is concave up when the 2nd derivitive of f(x) is positive

we are given f'(x), the derivitive of f(x)
we want to find where it is increasing AND where it is concave down

it is increasing when the derivitive is positive, so just find where the graph is positive (that's about from -2 to 4)

it is concave down when the second derivitive (aka derivitive of the first derivitive aka slope of the first derivitive) is negative
where is the slope negative?
from about x=0 to x=2
and that's in our range of being increasing
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4 0
3 years ago
5) a = 9, a = 34, n = 6
Stella [2.4K]

I need more info

Step-by-step explanation:

6 0
3 years ago
4. The area of the parallelogram<br>is 81.9 in? What is the height​
ipn [44]

Answer 96in2

Step-by-step explanation:

formula to find area = base x height

substitute the values

= 10 x 9

= 90 cm2

7 0
3 years ago
I will give brainliest to correct answer
FromTheMoon [43]

Answer:

D

Step-by-step explanation:

If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as

p(x)/x+k = q(x) + r/x+k

where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes x^{1} and no higher exponents), the remainder is a real number.

Therefore, p(x) can be rewritten as p(x) = (x+k)q(x) + r, where r is a real number.

The question states that p(3) = −2, so it must be true that

−2 = p(3) = (3+k)q(3) + r

Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.

A. −2=p(3)=(3+(−5))q(3)+0

−2=(3−5)q(3)

−2=(−2)q(3)

This could be true, but only if q(3)=1

B. −2=p(3)=(3+(−2))q(3)+0

−2=(3−2)q(3)

−2=(−1)q(3)

This could be true, but only if q(3)=2

C. −2=p(3)=(3+2)q(3)+0

−2=(5)q(3)

This could be true, but only if q(3) = −2/5

D. −2=p(3)=(3+(−3))q(3)+(−2)

−2=(3−3)q(3)+(−2)

−2=(0)q(3)+(−2)

This will always be true no matter what q(3) is.

Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.

The final answer is D.

6 0
3 years ago
1. find the sum of the measures of exterior angles, one at each vertex, of an octagon.
love history [14]
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5 0
2 years ago
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