13 01 5. Find a basis for the column space of the matrix 0 0 0 0 A 0 0 0 0 0 1 3 B {3 1 C { D { E { 1 0 0 0 0 0 0 0 0 0 0 1 -2 6 7 0 دیا 3 3 0 0 1 0 0 0 0 0 1} 0 دیا 3 -2 1 0 دیا 3 7 0 -2 1 0 3 -2 1 0 0 0 1 6 1} 3 1 1 -2 67 1 0 0 0 0 0

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

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Q: Find f(B)

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Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: This problem is related to the vector algebra. The problem is solved in the following image.

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

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Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

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Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: We will find the required.

Q: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: Find the basis for the Null space of the matrix 1 4 5 2 1 3 0 1 3 2 2 A = 2

A: A=14522130-1322 →R3→R3+R1R2→R2-2R1…

Q: Find the rank f the Mathisx by Normal form 3 5 1. 3 13 2. 2 8.

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Q: 8. Find the standard matrix for the orthogonal projections onto the column spaces of A 1 1 -1 –1 A…

A: orthogonal projection of column space of matrix A= A(ATA)−1AT

Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: |a,6,d e а a, b, d E R}. S2x2 b d Do three matrices 1 A1 = 0 1 1 0 A2 = A3 1 0 - 1 | form a basis of…

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Q: -9 4 4 1. Let A = -8 3 4 . Find an invertible matrix P and diagonal matrix D so that A = PDP-1.…

A: See the detailed solution below.

Q: |1 -2 4 3 1 1 -1 3 Let A be a matrix which is row equivalent to 0 1 1 0 1 0 0 0 -3 Find a basis for…

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Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

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Q: 1s) La L : A → R be the limsir operator Lip(z)) – p(0)r*+27/(c). Find the matrix A representing with…

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Q: A symmetric matrix satisfies M= M'. The set of 2 x 2 symmetric matrices S, with standard matrix…

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Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

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: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

Q: If the matrix of change of basis from the basis B to the basis B' is 302 A = 20 A. B. - 01 1 column…

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Q: Find an orthonormal basis for the column space of 7 -11 1 -4 -1 0 2

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Q: 3. Find the Jordan canonical form %]. 6 4 -69 (a) A= [- 1 241 1 2 (b) A= 4 5 (Ⓒ) A = [5 }]. -2 7

A: We have to find the Jordan canonical form of the matrix over ℂ. Note: There are multiple subparts.…

Q: 11. Construct a matrix with the required property or explain why this is impossible. (a) (.-) Row…

A: See the detailed solution below.

Q: 5. For the given matrix A, find a basis for the null space of A, and find a basis for the column…

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Q: [2 3 2] 10.) Is A=|0 7 6 an invertible matrix? Explain [5 5 4]

A: We have to solve the problem

Q: 28. True or false (give a good reason)? (a) If the columns of a matrix are dependent, so are the…

A: 1a) False 1b) False 1c) True 1d) False

Q: 5. Construct a matrix with the required property or explain why this is Impossible. (a) Column space…

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Q: tind an orthogonal boasis for the column Space of the matrix. An orthogonall basis for the of -8 4…

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Q: If i had a vector X what was a 2x4 Matrix being |818-2 | | -6 1-6 -2 | How would i find the…

A: let A = 818-2-61-6-2   reduced Echelon form is rref= 100-20110    Equations Form…

Q: 5. Construct a matrix with the required property or explain why this is impossible. (a) Column space…

A: We will be using required definitions.