a5=0 and a15=4 what is the sum of

Usman Zahid 2022-07-24

a5=0 and a15=4 what is the sum of the first 15 terms of that arithmetic sequence

You can still ask an expert for help

Want to know more about Matrix transformations?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-13

For the matrix A below, find a nonzero vector in the null space of A and a nonzero vector in the column space of A
A=[2359891121431727] 
Find a vector in the null space of A that is not the zero vector 
A=[3201]

asked 2021-09-13

Suppose that A is row equivalent to B. Find bases for the null space of A and the column space of A.
A=[12511324515212045365192]
B=[12045005780000900000]

asked 2021-09-18

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space.
A=[154310121000000]

asked 2021-12-17
Find k such that the following matrix M is singular.
[33367611+k1615]
asked 2022-06-26
Let V be inner product space.
Let e 1 , . . . , e n an orthonormal basis for V
Let z 1 , . . . , z n an orthonormal basis for V
I have to show that the matrix represents the transformation matrix between e 1 , . . . , e n to z 1 , . . . , z n is unitary.
asked 2022-07-08
Consider the 4-by-4 matrix M = M 0 + M 1 , where
M 0 = α ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) and M 1 = β ( 0 γ 0 γ γ 0 γ 0 0 γ 0 γ γ 0 γ 0 )
where α and β are constants and γ = γ x + i γ y is complex.
Is it possible to unitary transform M into block off-diagonal form M B ?
Namely, I want to find a unitary transform U so that I can write down M B = U M U (here U is the conjugate transpose).
Explicitly, the required block off-diagonal matrix is (in general form)
M B = ( 0 Q Q 0 ) where Q = ( Q z Q x i Q y Q x + i Q y Q z )
Is there a general recipe to find such a unitary transformation matrix U which leads to the block off-diagonal form, M M B ?
asked 2022-07-03
Consider the m × m-matrix B, which is symmetric and positive definite (full rank). Now this matrix is transformed using another matrix, say A, in the following manner: A B A T . The matrix A is n × m with n < m. Furthermore the constraint r a n k ( A ) < n is imposed.
My intuition tells me that A B A T must be symmetric and positive semi-definite, but what is the mathematical proof for this? (why exactly does the transformation preserve symmetry and why is it that possibly negative eigenvalues in A still result in the transformation to be PSD? Or is my intuition wrong)?

New questions