Factoring polynomial expressions.

Factor the following: a) 3y^2-3 b) 25-16x^2y^2 c) (x+y)^2-z^2 d) (x-3)^2-9 e) t^2-2t-3

Linear Algebra -- Linear Transformations

Let L be the linear transformation mapping R2 into itself defined by L(x) = (x1*cos alpha - x2*sin alpha, x1*sin alpha + x2 cos alpha)T Express x1, x2, and L(x) in terms of polar coordinates. Describe geometrically the effect of the linear transformation. Thanks very much.

Linear Algebra -- Kernel and Range

Determine the kernel and range of the following linear transformation from R^3 into R^3. L(x) = (x1, x2, 0)^T Determine the kernel and range of the following linear transformation from P3 into P3. L(p(x)) = p(x) - p'(x) Thank you!

Linear Algebra -- Kernel and Range

I don't understand this kernel and range stuff. Determine the kernel and range of each of the following linear transformations from R3 into R3. (a) L(x) = (x3, x2, x1)^T (b) L(x) = (x1, x1, x1)^T And determine the kernel and range of each of the following linear transformations from P3 into P3. (a) L(p(x)) = xp'(x ...continues

Linear Algebra -- Orthonormal Sets

Please see problem #1 of the attachment. If you show me how to do #1 (the answers are a and d, by the way) I'll probably be able to do #2. Thanks!

Linear Algebra -- Inner Product Spaces

In C[-pi, pi] with inner product defined by (6), show that cos mx and sin nx are orthogonal and that both are unit vectors. Determine the distance between the two vectors. (6) (f,g) = (1/pi)* the integral from -pi to +pi of f(x)g(x)dx This is all from Linear Algebra With Applications by Steven J. Leon, Sixth Edition. Than ...continues

Investigating trios.

Q. Three whole numbers, greater then zero can be used to form a trio. example: (1,2,2) is a trio whose sum is 1+2+2=5 And (2,1,2) is a different trio whose sum is also 5 How many trios can you find with a sum of 5?

Understanding reference decimal radians.

How do I find reference decimal radians?

Understanding sequencing and fraction differences.

Context: It would normally follow on from work on sequences and fractions Question: Ruth was investigating fraction differences. She wrote down this sequence of fractions: 1/1, 1/2, 1/3, 1/4, 1,5 1,6 ... ... Then she worked out the difference between the consecutive fractions: 1/2, 1/6, 1/12, 1/20, 1/30, .. .. Sh ...continues

Novel method in single digit division (without the use of a calculator).

What is 122 divided by 3?