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: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

A:

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

A:

Q: Prove that (a) C(B) C Nul(A), where C(B) denotes the column space of B. (b) rank A + rank B < 5

A: Given that A is a 3×5 matrix and B is a 5×6 matrix. Also AB=0.

Q: Let A be a matrix whose entries are integers, and det A=1. 4 : Show that the entries of A-1 are all…

A: given ,det A = 1

Q: det (–3(A" A-²)*) Consider matrix A of order 3, the value of corresponds to: 1 a) –7 - 1 b) –3 c) –3…

A: For the solution of the problem follow the next step.

Q: 1 A = )Find the rank of a matrix 7 17 1 - 2 | 3.

A:

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: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: s elect the matrix correspon ding to the form QLX,, Xz, Xx, Xu ) = - 2x1²+ 5 X; - 7×3 -4 Xú - 6Xi Xz…

A:

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

A:

Q: Q2) In each of the following cases, find the matrix A for which [v]D=A[v]B a. B={1, 2x, 4x²-1} and…

A: Here we use the definition of the change of basis matrix. For that we first write the basis elements…

Q: Determine whether A is diagonalizable. A = (D, P) = 0 2 2 220 OYes O No Find an invertible matrix P…

A:

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

A:

Q: O Consider a non-singular n x n matrix A. Let A = inf{||SA|| : A+ 8A is singular}. Show that 1 A…

A: We are given a non-singular n×n matrix A and ∆ = inf{||δA|| : A+δA is singular} And we have to show…

Q: 5) Consider the following matrix: A = 1 2 20 -1 1 030 (i) Compute the adjoint of A. (ii) Use this to…

A:

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

A:

Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: 1 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

A:

Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

A:

Q: 1 4 [-1 Form the Matrix Ak? 3.Let Matrix A = 2 3 and k be any scalar b = -4. -3]

A: We need to find Ak.

Q: ´ be the following matrix: [1 1 1 J =1 2 [1 4 x ] Find Compute the determinant of J in terms of x…

A:

Q: 1. Consider the matrix and and Monde Cole 2022 202) Mesh Colleg 202C) Mona that 1 1 0 101 0 1 1 Mo…

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: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

A: We need to solve the determinant and find the value of x.  Now, if we have a 3×3 matrix…

Q: Prove: For any square matrix A, det(A) = det(A¹).

A: We know Transpose of matrix is found by interchanging its rows into columns or columns into rows

Q: USE THE SAME MATRIX "E" from above. Verify E x inv(E) is a 4 x 4 Identity Matrix. Fill Up the Empty…

A:

Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

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…