1. Let A be a square matrix whose Jordan canonical form is '1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 00 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 10 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2, 0 0 0 0 0 (a) Is A nonsingular? Explain. (b) Write down all the eigenvalues of A and their algebraic and geometric multiplicities. (c) Let K be the nullspace of (A – I)? where I is the 9 x 9 identity matrix. Evaluate dim K.

Q: = [aij), whose entries satisfy the conditions fi +j if i sj aij= ( 1 if i >j is: The 4 x 4 matrix 4…

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Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

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A: Find your answer below

Q: 9. Prove that the spectral norm of a symmetric matrix is the same as its spectral radius.

A: Solution :-

Q: Find the rank of the following matrices.

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Q: 2. Suppose that B = 10 1 [000] 10 1 such that TB: R3 -> R3 Determine: (1) ТВ Kernel (TB) Range (TB)…

A: Here given matrix as B=101000101 This matrix is the standard matrix of the linear transformation TB

Q: Consider the BVP u" =u+2,0<t<1, u(0) =1. u(1) = -1 Using the central difference quotient and 4…

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Q: 3. Suppose a matrix G that performs a 3-entry rolling sum of a vector x, i.e., GX = (X₁, X₁ + X2, X1…

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Q: 1. Find a matrix P that diagonalize matrix A. Compute B = P-'AP 1 0 1 A = |0 1 1 1 1 0

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Q: [1 0 [9 0 01 c) A-2 = |0 4 0 Lo o 1l 9. Find a matrix A that satisfies a) (3.4) =0 -1 1 |0 0 -1| 2.

A: ANSWER :

Q: 18 (a) If P is the 2 by 2 projection matrix onto the line through (1, 1), then I – P is the…

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Q: 10 - Which of the following matrix represents the symmetric closure of R? (1 0 1 0\ 0 1 0 0 0 0 1 1…

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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: 200 2. The matrix4 1 0has the inverse matrit 20 1 2007 /2 0 07 -/4 10 /2 0 1 /2 0 0 -1/2 0 0 410 6.…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: There exists a 7 x 6 matrix A with rank(A) = nullity(A). A) True B) False

A: Suppose that A  be  the  matrix of size 7.Recall  Rank-nullity theorem:  Let  A   be  a  matrix  of…

Q: 9. The dimension of the nullspace of A is called the nullity of A b. nullity(A) dim(RS (A)) a.…

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Q: Consider the 4 x 5 matrix 1000 2 00300 0000 0 0 2 0 0 0 A singular value decomposition of this…

A: Since in singular value decomposition matrix U∑v*, where ∑=diag(σ1, σ2,σ3....σn);…

Q: 2. (a) Construct a matrix whose null space consists of all linear combinations of vectors (3, 2, 0,…

A: Null space and matrix

Q: Let A = [ 0.7 3 ²] 0.2 0 and u = [80, 30]¹.

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

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Q: 2. Use row operations to transform the following matrix 1 0 -1 1 012 4 in the form 001 −1 1 2 4 b…

A: Given matrix is

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Q: b). i) 1 Let A, B Man (C) be two square matrices. 14 A~ B. eigenvalues iii) - Explain what it means…

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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: * Proferties of Deta If (Alis a square matrix for eXamlle A=

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Q: 5. Use spectral decomposition to orthogonally diagonalize the matrix A = 5 10 {]. 5

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Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0) 1 0 0 1 1 0…

A: The set is A = {a, b, c, d}. The matrices representing the relations R and S, respectively, are as…

Q: (i) Find the change-of-basis matrix Ps,-E and then use it to find the component vector [C]s, of -…

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Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.