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...

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!