22 Q.4 Using the matrix: X = 2 4, Calculate: 2 6 M=(I₂ −X(X¹X) ¹X¹) and show that M is a symmetric and 3 idempotent matrix.

Q: Q: Determine if the following system is consistant q using matrix ? X2 - 4X3 2X1 -3X2 +2X3 =l 5x,…

A:

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: [2a11 5a12 Let A = |2a21 5a2 -3a23 2a31 5a32 -3a33 diagonal matrix and neither B or D is equal to…

A: The given matrix isA=2a115a12-3a132a215a22-3a232a315a32-3a33.We have to factorise A into A=BD where…

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Let A be an invertible 3 by 3 matrix. Assume that PA²P-15ATA². = Then det(A) =

A: Step 1:   Step 2: Step 3: Step 4:

Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

A:

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

A:

Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: Suppose A is a symmetric matrix. (Au)" : u"A

A:

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: Find a 2 x 2 matrix such that [3]==1] (incorrect) 4 -2 -2 Answer(s) submitted: C

A:

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

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

Q: n 2. Check whether the matrix A- 2 Check whether the matrix A (0 is Hestnitian and Unitary matrix or…

A: The detailed solution is given below Thank you

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

A:

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

A:

Q: 3. Find m and n so that the matrix below is symmetric:

A:

Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

Q: 3.) Find the inverse matrix? 2 Use the adjugate of A = 0 -2 1 to find A-1 | 1 0 0 - 2 3.

A:

Q: determine the diagonalizing matrix: X1 = λαι X2 + X3 = λχη – X2 + X3 = λx3

A:

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: If A is a positive definite matrix and B is positive semi-definite, show that trace (AB) 2 O with…

A:

Q: Exercise 5H. Let X be a square matrix with real entries such that XTX = I. Argue that det(X) = +1.

A: Clearly X is orthogonal matrix . And the determinant of orthogonal matrix is 1,-1

Q: 6. 1 4 If w = -3 E span 2 then x = 1 4 3 Select one: True 21 False

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: Explain why for any matrix A, AA' exists and prove that AA' is a symmetric matrix

A: Let A is any matrix of order m by n Am×n    and   Atn×m Now  AAt exists of order m by m To prove…