This one is easy think about trig identities and try to express one function in terms of the others. See which function is superfluous.physicsss said:I'm stumped by this problem:
let W be the subspace of C[0,1] spanned by S={sin^2(x),cos^2(x),cos2x}
a) explain why S is not a basis for W
it's because S not linearly independent
b) find a basis for W
please help me with this one...
TIA.
Subspace base math is a mathematical concept used in linear algebra to solve problems related to vector spaces. It involves finding a set of vectors that can span the entire space and form a basis for the subspace.
Subspace base math has many applications in fields such as physics, engineering, and computer science. It is used to solve problems involving systems of linear equations, to analyze data sets, and to design algorithms for computer graphics and machine learning.
The first step in finding a subspace base is to determine the dimension of the subspace. This can be done by finding the number of linearly independent vectors in the subspace. Then, a set of linearly independent vectors that span the subspace can be found using methods such as Gaussian elimination or the Gram-Schmidt process.
A subspace base can be represented as a matrix, with each column representing a vector in the subspace. Alternatively, it can be represented using a set of coefficients for each vector, such as in a linear combination.
Subspace base math allows for the efficient and accurate solving of problems involving vector spaces. It also provides a powerful tool for analyzing and manipulating data. Additionally, it has many practical applications in various fields, making it a valuable skill for scientists and engineers.