11. 1 2 3 2 6 3 0 6 -6 -1 -2 -9 -1 0 7 0

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

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Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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Q: Find the LU factorization of -1 -5 -4 A = -5 -26 -18 That is, write A = LU where L is a lower…

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Q: Give an example of a matrix M where MMT and MTM are not equal matrices.

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Q: Define Square matrix?

A: A matrix is the arrangement of data in rows and columns.

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: If A is an orthogonal matrix, find a QR factorization of A

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Q: Construct a 3 by 3 matrix whose column space contains ( 1, 1, 0) and ( 1, 0, 1) but not (1, 1, 1).…

A: Column space: The set of columns of a matrix which are linearly independent is called the column…

Q: 6 and u = 5 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A*…

A: Please check step 2 for the solution.!

Q: Show that every diagonalizable matrix has a square root.

A: Square Root Matrix of a Diagonalizable Matrix is Diagonalizable. A is diagonalizable. Therefore,…

Q: Show that for a square matrix A, AAT is a symmetric matrix.

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Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

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Q: Give the 4 x 4 matrix that rotates the points in R° about the y-axis through an angle of 60°. The 4…

A: Let a point in ℝ3 is rotated about y-axis through an angle θ=60°.

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: Find the matrix B such that 2AT+3B=0.

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Q: What is a row matrix?

A: A matrix having only one row is called a row matrix.For example