Compute the inverse and find the condition number in sum norm of the Hilbert matrix 11 1- 1819 -10 9 10 1 1 11 1 11 12-

Q: Find a basis for the space of 2 × 2 lower triangular matrices. Basis =

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Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: M2,2 is the vector space of all 2 x 2 matrices. List the o element of this vector space.

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Q: This is a linear algebra question Suppose A is a square matrix with Col(A) is a subset of Null(A).…

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Q: Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. 7 3. Let y =…

A: Find the orthogonal projection of the vector y on u., which will give the y^. Then to find z,…

Q: If the eigen vectors of a 2 x 2 matrix A corresponding to the eigen values –1 and6 are 2…

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Q: A function multiply_A(x) that computes Ax, the result of multiplying a matrix A ∈ Rm×n by a column…

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Q: If matrix A is full row-rank, then use SVD to prove that the pseudo inverse is given by A+ =…

A: According to null matrix singular decomposition, a matrix A can be written as, A=U∑V* Then use the…

Q: Construct six linearly independent 3 by 3 echelon matrices U1, ... , U6.

A: To Find : Construct six linearly independent 3×3  echelon matrices.

Q: Create a world transform matrix that translates by 3, 5, 7 and rotates 80° about the x-axis.

A: Detailed explanation mentioned below

Q: Put the following matrix in rational canonical form: 1 1 1 0 -4 -1 5 2 -3 3 1 1 1

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Q: Use the Gramm-Schmidt algorithm to find an orthogonal basis for the column space of the matrix 1 0 1…

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Q: What is a singular matrix

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Q: Find a basis of the linear space V of all 3 x 3 matrices A for which both | - A 1 and are…

A: We have to find the basis of linear space V.

Q: Find the LDU factorization of L = That is, write A = LDU where L is a lower triangular matrix with…

A: Given We need to find the LDU factorization of matrix A.

Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

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Q: 44. Let A and B be n x n matrices, each with n distinct eigenvalues. Prove that A and B have the…

A: Given that A and B are two n×n matrices with distinct eigenvalues.   Let  λ1 , λ2, λ3,…

Q: on and multiplication defi

A: Given as, GL2C is set of invertible matrices.

Q: matrix A if (A" – 21)* = } Determine the matrix A if %3D

A: Given,             12AT-2I-1=1234To find : The matrix A.

Q: 1) Consider the "elementary matrices" 7 01 Elry - [88], Es-in-=[68], and EET-1 (8) E5-123 : 050 =…

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Q: Find orthogonal bases for the null space and for the range of the matrix  [1, 0, 0, 3; 1, 1, 0, 4;…

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Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / infinity, where…

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Q: Suppose A,B,C are each nxn invertible matrices. Show (ABC) CBA.

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Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

Q: Apply Gram-Schmidt method to change {{:)} into an orthonor- mal basis {u¡, u2} of R² .

A: We have to find the orthonormal basis for the given set.

Q: The null space for the matrix is spanned by the vector 2 -1 4 5 4 0 5 6 2 4 -1 1 0 1 1

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Q: d) All of the above LQ9. Suppose A is the 4 by 4 identity matrix with its lAst column renoved. The…

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Q: 3) Develop matrix form of the quadratic spline polynorhials for these data po: (1, 1), (2, 3), (3,…

A: Given: 1,1,2,3,3,5,4,2 n=4

Q: If the column space of a 3x3 matrix consists of all vectors b=[b, b2 b3] such that b,+ b2= 3b3 then…

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