2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A- with A and / 1 2 2 ii. Be A = 2 1 2 2 2 1 ii. Ве 4 Calculate: 4 and 4! %3D ii. Show that the matrix given in section-ii satisfies the equation in section-i and check that 4 obtained in section-į is the same as that obtained in section-ii.

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

A:

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: Verify that if r < s, then rows rand s of a matrix can be interchanged by performing 2(s - r) - 1…

A:

Q: 2) does the following matrix is orthonormal and orthogonal? Why? R = 2

A: Orthogonal and orthonormal matrix

Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

A:

Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

A:

Q: Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is…

A:

Q: Find 6×6 matrix a, that satisfies the stated condition. Make your answers as general as possible by…

A: Let the genral 6*6 matrix is given by…

Q: Let A be an m × n matrix. Under what circumstances will ||A||2 = ||A||F?

A:

Q: 5. Verify that the product of the non-singular matrix and its inverse from the previous problem is…

A: (5) Given matrix A=32−22 and its inverse is A−1=1102−223. We have to verify that AA−1=I2…

Q: ve that for every matrix A, (AT)T = A

A: We have to prove that transpose of A transpose is A.

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

A:

Q: if A is m xN matrix pivot in every row, then Ax-b has that has a a unique solution for each b in Rm

A: The given question can be solved as shown in step2.

Q: Compute the matrix exponential e At for the system x' = Ax given below. x'1 = 35x1 - 34x2, x'2 =…

A:

Q: Find x such that the matrix is singular. A- -2

A:

Q: Show that the matrix; is singular

A:

Q: Solve for the matrix X if AX(D+BX)-! = C. Assume that all matrices are n x n and invertible as…

A: It is given that AXD+BX-1=C. It is required to solve for the matrix X such that all matrices are n×n…

Q: 4. Consider the 3 x 2 matrix A such that A - and A (a) Write down A. (b) Is A singular? Justify your…

A: 4. The given equations are,A.12=201 and A.21=201

Q: Find all aclh for which the matrix A = [at3 2 b non-singular.

A:

Q: 2 - matrix A and that h(T) = T? – 2T – 7 -

A:

Q: Solve for the matrix X if AX(D + BX)-! = C. Assume that all matrices are n X n and invertible as…

A:

Q: A = (aij) be a 10 x 10 positive definite matrix with Cholesky factor R = pose that a11 = 9, a12 =…

A:

Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

A:

Q: Let  A be a symmetric tridiagonal matrix (i.e., A is symmetric and aij = 0 when ever |i−j| > 1). Let…

A:

Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

A: Introduction: If the transpose of a square matrix with real numbers or elements equals the inverse…

Q: For which valua of k does the matrix 1 have real eigrenvalue of one multiplic ety 2 a to

A:

Q: 4 Compute x using the vectors w = -2 and x = (Simplify your answer. Type an integer or simplified…

A:

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: 1 if k = i and l = j if k = j and l = i if k = l but k # i, j 1 (Si3)ke = 1 otherwise.

A:

Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: 3- If x=[ 26 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…

A: X=[  2 6 12;15 6 3;10 11 1]

Q: Suppose A = UDVT where U and V are n x n matrices with the property that UTU = I and %3D vTV = I,…

A:

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

A:

Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

A:

Q: I1,I2,I3 of th

A: Here we have;  11I1+4I2+3I3=-4-15I1+4I2+4I3=163I1+4I2+17I3=3 let;  AX=B  where  A=1143-15443417,…

Q: 10 choose a,b,c,d

A: 1. Option a is wrong as the columns of D are LI hence solution will be unique if exists. 2. Option b…

Q: From S = QAQ" compute the positive definite symmetric square root QVAQT of each matrix. Check that…

A:

Q: 2. Choose the rank of the matrix AT

A:

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Q3/create a matrix A and 1- add fourth & fifth rows equal to [1 2 3] by using [1 2 3] A= 4 5 6 L7 8…

A: Here is the solution:

Q: Suppose that {v1, v2,..., vn} is a linearly independent set of vectors in Rn. Show that if A is an n…

A: Let's suppose we have a linear relation:…

Q: Determine whether the matrix is invertible. 5 5 -5 8 2 -8 -7 0 7 Also find AT

A:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then O a. QQT = I O b. QQT + I OCQT = Q1 Od.…

A:

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…

Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…