(a) Describe the kernel and the image of Jn. (b) Use this to show that J, is diagonalisable when n # 0 in F.

Q: Explain why the columns of an nxn matrix A are linearly independent when A is invertible.

A: The objective of this question is to understand the relationship between the invertibility of a…

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many…

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Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: Let A and B be two square matrices of the same size. Suppose B is singular. Explain why AB is also…

A: Given Information: A and B are two square matrices of same size. Suppose B is singular. To show: AB…

Q: elementary

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Q: 4 Is the matrix A = -3 O Yes O No 1-3 1-3 2 -1 -4, invertible?

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Q: hat is a matrix

A: Matrix:

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: why is the matrix like that?

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Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Provide an example of an elementary matrix for each of the three types of row operations and clearly…

A: The three types of elementary row operations on a matrix : (1) Interchange two rows (2) Multiply…

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: Prove that the identity matrix cannot be the product of three row exchanges ( or five). It can be…

A: An identity matrix is a square matrix of any order which contains on its main diagonal elements with…

Q: Are the dimensions of the bases of a nxn Matrix always n? Can they be n - 1 or n + 1? Is it the same…

A: In the matrices, the dimensions of the bases are related to the vector spaces they represent.  1.…

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: is there any way you could write this on paper? or just write the matrix part on paper

A: We have the system of equations as x1+x2+x3=56x1+7x2-3x3=5

Q: Is the matrix A invertible -1 2 3 -6 O True O False

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Q: What is the term matrices

A: Matrices :- A matrix is an ordered rectangular array of numbers or functions. The numbers or…

Q: Please compute the next matrix

A: The solution is provided for A. We shall solve B and C.