Let D be a 4 × 4 matrix of the following form: [a11 a12 b11 b12 a21 a22 b21 b22 D = 0 0 C11 C12 0 0 C21 C22 That is D is "built up" of the four 2×2 matrices consisting of the together with a 2 × 2 matrix of 0's. aij bij and Cij coefficients, Show that: det (D) = det (La a11 a12 C12 a21 a22 C21 C22

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

A:

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Find the (1, 1) entry of the matrix product XY using the matrices below: a X = b and Y = | c 1 -1 d…

A: To find  entry of the matrix product  using the the matrices below. and  and , and .

Q: Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

Q: Let A and B be two 4x4 matrices with rank(A)<4. Then rank(AB)=4. E ((C Select one: OTrue OFalse

A: We know that  Rank(AB) = min{rank A, rank B} Since Rank A &lt; 4

Q: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: Select all of the following that are true for all nxn matrices A and B. AA²-A²A (A+BILA-B)-A²-B²…

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Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: d) Consider the following matrices: and B- 2 Find: A- i) (2AB) -1

A: Given A = 1-32-4 and B-1 = 21-11

Q: a4 a1 Let V1 (3).. b4 be four vectors in R³. b₁ b₂ V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix…

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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: Find a 3 × 2 matrix A and has LU factorization where L is diagonal.

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