# bases

1. ### Finding the bases for range and kernel

Hi, I have the following problem: A linear transformation G: P2 ---> P2 defined by G(h(x))=2x h’’(x) + h’(x) I need to find bases for the kernel and range of T. I understand the definition of kernel means that we have to set it equal to zero and the coefficients must all equal zero, but there...
2. ### Bases

Hello The question : Let be a basis of R^3. Are any of these two sets also a basis of R^3? My thoughts: The vectors a b c are linearly independent - given. Therefore they are not the same. So both 1. And 2. Are bases of R^3 because none of the vectors in those sets is a linear combination...
3. ### Bases, Exponents, and Digits

Question: What's the smallest positive value of k such that the base nine representation of $\left ( 27_{ten} \right )^{k}$ has exactly 9999 (base ten) digits? Work thus far: I know that in base ten to find the number of digits you just take the common log and round up, and I'm guessing that...
4. ### Solve each exponential equation using like bases.

e^(-x+6)=e^x -x+6=x = 0=6 What am I doing wrong here?
5. ### Two bases for this subspace

I need to give two bases for the following subspace. I'm able to find the spanning set, and thus, a possible basis. Would a second possible basis be the following: 2 0_____ 0 4_____ 0 0 0 -2____ 0 0_____ 3 0
6. ### Finding subspaces and bases of vector bases

Hi guys I am having trouble with the following question S= {(2,-1,4), (1,1,-1)}, T= {(x,y,x,-2y):x,y\in R} a)Show that S\subseteq T and write down a vector in R3 ​that does not belong to T b)Show that T is a subspace of R3 Is the first part of the question asking to prove that S is a...
7. ### Logarithm Bases Portfolio

let log(subscript)aX=c and log(subscript)bX=d find the general statement that expresses log(subscript)abX in terms of c and d test the validity of your general statement using other values of a, b, and x discuss the scope and/or limitations of a, b, and x explain how you arrived...
8. ### Desperately need help with three questions concerning images, kernels, bases, etc.

Please see this link: Linear Algebra Questions - TexPaste There are three questions. Shouldn't take longer than 10 minutes. Please give me answers for now. When I'm working it out, if there's anything I don't get, I'll come back for guidance. Thank you so much.
9. ### Basic concepts on bases

1. Can the basis be {(1, -1, 0, 0)T, (0, 0, 1, -1)T}? I wonder if the ans is right. Here x2, x4 are supposed to be the free variables, and x1, x3 as dependent variables; but the ans used x1, x3 as free variables. Or am I wrong???? Both can be bases?? 2. When asked to find a basis, we just...
10. ### Addition in Other Bases

When we add 2 + 4, the answer is 6. The addition above is called addition in base 10, right? How do we add in other bases? For example, how do we add 2 + 4 in base 2? How about in base 3?
11. ### Multiplication and Subtraction of logs with different bases.

\text{If }a=\log_{12} 18, b=\log_{24}54\text{, then find the value of }ab+5(a-b) I am trying in different ways to equalize the bases. But I can't do anything as the bases are unequal.
12. ### Linear Algebra-Transition Matrices

Hey guys, I'm after some help on this problem. Help would be much appreciated.
13. ### Bases for R2

Course: Linear Algebra So I have the set \left\{(0,0) , (1,3)\right\} which I will call S. I'll have the system: c_2 = x_1 3c_2 = x_2 Which gives me c_2 = x_1 = \frac{1}{3}x_2 Can this mean that span(S) = R2? Is the zero vector redundant?
14. ### Determine the matrices that represent the following rotations of R^3

I need to determine the matrix that represents the following rotation of $R^3$. (a) angle $\theta$, the axis $e_2$ (b) angle $2\pi/3$, axis contains the vector $(1,1,1)^t$ (c) angle $\pi/2$, axis contains the vector $(1,1,0)^t$ Now, I would like to check if I got the right answers...
15. ### Logarithmic equation with different bases

Would appreciate some guidance on the problem below: Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number To solve I tried converting to a single base using Log[base A]x = Log[base B]x / Log[base B]A which gives: Log[base 25](6x + 25) = Log[base 5](6x + 25) / Log[base...
16. ### Grobner Bases - Second question on D&F Proposition 24

I am reading Dummit and Foote Section 9.6 Polynomials in Several Variables Over a Field and Grobner Bases. I have a second problem (see previous post for first problem) understanding a step in the proof of Proposition 24, Page 322 of D&F Proposition 24 reads as follows: Proposition 24. Fix a...
17. ### Grobner Bases

I am reading Dummit and Foote Section 9.6 Polynomials in Several Variables Over a Field and Grobner Bases. I have a problem understanding a step in the proof of Proposition 24, Page 322 of D&F Proposition 24 reads as follows: Proposition 24. Fix a monomial ordering on R= F[x_1, ... , x_n]...
18. ### Find the Matrix for T Relative to the bases {1, t, t^2} and {1, t, t^2, t^3}.

I've done part a and b. I'm stuck on c and don't know how to go about it. Can somebody help please?
19. ### Need help finding one of the bases

I have a trapezoid with a top base (b1) of 10 and a height of 5. Considering the area, find b2 Do I need to find the area first? If so, can someone explain how I go about that. You don't need to give me the answer, but I'm not sure where to start. Thanks!
20. ### Solving Equation: Exponent with different bases

Hi, need help solving this problem! My brain is very rusty right now, and I just can't seem to figure it out: Ax-1 = 9 -181-x where A is a constant. Solve for X Please help and explain how to derive it. Thanks in advance!