Which of the following subsets of R3X3 are subspaces of R³×³? A. The invertible 3 x 3 matrices B. The 3 x 3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries) C. The 3 x 3 matrices of determinant 2 D. The 3 x 3 matrices A such that A 4 0-0 7 E. The non-invertible 3 x 3 matrices F. The diagonal 3 x 3 matrices

Q: Determine which of the following matrices are invertible. Try to perform as few computations as…

A: As per bartleby guidelines we only give first three question answers.

Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

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: Consider the set of matrices 0 S = {(a+b):abER} a, bЄR

A: Step 1:Here given that S={(ab​0a+b​):a,b∈R}as sub ring of of ring  M2×2​(R). Step 2e) :we have to…

Q: Select all statements from below options that are true for ALL invertible n x n matrices A and B DA.…

A: To find correct option from given question.

Q: Prove or disprove the following statements  i. If A and B are two n×n matrices, then (A + B)^2 = A^2…

A:

Q: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

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: [2 Let A = Find all matrices of the form B = that commute with A. P In other words find all matrices…

A: We have to do both the matrix multiplication.

Q: Determine which of the formulas hold for all invertible n x n matrices A and B OA. (A+ B)² = A² + B²…

A:

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: Let A and B be invertible n * n matrices. Then the inverse of ABA-1 is Select one: O a. ABA-1 O b.…

A: • The inverse of ABA-1 is AB-1A-1. • The option c is correct. Explanation:

Q: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

Q: If B non-singular 2x2 matrices and k is a non-zero scalar. Which one of the following expressions is…

A: Please see the solution in the next step

Q: Let A and B be 3 x3 matrices, with det A = 2 and det B = 6. Use properties of determinants to…

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Q: Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A…

A: