matrix that does not have a determinant

Related BrainMass Solutions

• Matrix Expressions : Factorizing

  To find that we have: -cR1+ R2 ---> R2, so R2= [0 a- c ab- ac- bc] and that does not change the determinant. Also, we have: R1+ R3 ---> R3, so R3= [0 0 a+ b+ c].

• Matrices

  Cramer's Rule states that the solutions for the unknown variables are: Since we have already found the matrix A, we can find the determinant of the matrix as follows, I have used the first row (I will not go into details with the

• Square Matrix with Determinant Equal to 0 and Basis for a Solution Space

  154738 Square Matrix with Determinant Equal to 0 and Basis for a Solution Space 1) Let A be a square matrix with determinant equal to 0.

• Properties of Elementary Matrices

  So you need only show that every elementary matrix is square and has a nonzero determinant.

• Proof: 2x2 matrix invertible iff det not equal to 0

  Assume that the matrix is invertible and show that ad-bc is not zero. 2. Assume that ad-bc is not zero then show that the matrix is invertible. Note: a. To be invertible means that the inverse of the matrix exists i.e.

• quasi-concavity

  f_n 0 | have border-preserving principle minors determinants of order k that alternate in sign. The expert prove that quasi-concavity does not imply concavity.

• Systems of Equations : Real World Situations and Solving Determinants

  The process repeats itself until all minors have dimension 2 x 2, where the determinant can be easily calculated as . Note that the formula works for 2 x 2 matrix as well. Let us consider an example of 4 x 4 matrix A.

• Prove that pivot columns of matrix A form a basis for C(A).

  So, |C| is not zero, and so |B| is not zero either. It is proven that pivot columns of matrix A form a basis for C(A).

• Determinant of the Van der Monde Matrix

  We will prove that determinant A, denoted by Det(A), is Det(A)= = (*) Proof. n=2, Det(A)= , so (*) holds for n=2. Assume that (*) is true for all , we will show that it is true for n+1.