Prove by induction the Determinants of all Cartan matrices corresponding to simple finite dimensional Lie algebras of classical type.

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  The determinant a A…

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Q: ) Compute the determinants of all the leading principal submatrices of A. Explain why or why not A…

A: We know that, A n×n matrix is symmetric if and only if A=AT, where AT is transpose of matrix A.

Q: Each of the following properties defines a set of real n \ n matrices. Find out which sets are…

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Q: A matrix A with the property A² = A is called idempotent. Find all possible values of the…

A: Given a matrix A with  the property A2 = A is called idempotent.To find all possible values of the…

Q: Suppose that A is an n x n matrix and that A is invertible. Select all of the following statements…

A: Some Important notes:-Note‐1→a set of K linearly Independentvectors in ℝK  forms a baisi of  ℝK  and…

Q: Exhibit a basis for M2x2, the vector space of all 2 x 2 matrices of real numbers.

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Q: If v is an eigenvector of A, then ū is an eigenvector of A".

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Q: 4) Let M₂,2 denote the vector space of 2x2 matrices and W be the set of all 2x2 matrices A= such…

A: Recall  the  definition  of  a  basis  of  a  vector  space :  Let  V be  a  vector  space  over a…

Q: Which of the following sets are closed under scalar multiplication? (i) The set of all vectors in R2…

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Q: {(; ?)· (: :)· (; )} 1 Consider the ordered basis B for the the set of symmetric -1 2 x 2 matrices…

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Q: If A is an eigenvalue of A, then A is an eigenvalue of AH.

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Q: A = 3 1 2 7 -1 4 Find an orthonormal basis of the row space of A. }.

A: The answer is given by using gram Schmidt process as follows

Q: 3/0 30 0-3 2 10-124) A = 2 2 I converting A to an upper triangular matrix. Ist > Compute IAI by

A: When all the entries below of main diagonal are 0 then matrix is upper triangular matrix .. And…