Let B = a b c d be an arbitrary matrix in M2×2(F). (a) Use the formula for the determinant of a 2×2 matrix to give an explicit formula for the characteristic polynomial of B. (b) Show that B2 ∈ tr(B)B + det(B)I2 = 0, where 0 denotes the zero matrix. (Hint: Use the Cayley-Hamilton Theorem.)

Q: True or False? The cross product i xở can be calculated with the determinate of a 5 x 3 matrix. The…

A:

Q: 4. Consider w = and v =. (a) Write z = as a linear combination of w and v. (1 2 3 (b) Consider the…

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Given :-  The given T is a linear transformation from ℝ2 into ℝ2.  Tx1, x2 =4x1-5x2,-4x1+7x2 To…

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Given T(x1,x2)=(6x1-5x2,-6x1+8x2) So T(1,0)=(6,-6)T(0,1)=(-5,8) So the standard matrix for T is…

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Here, the given T is a linear transformation from ℝ2 into ℝ2. It has to be determined T is…

Q: Let A, B and C be three n x n invertible matrices with A² = A. Solve the following matrix equation…

A: Given ,  are three  invertible matrices with    .And    Since  are invertible matrices, exist  .

Q: 1. Consider (a) ê (c) E M = 135 247 89 a | Compute |M| by unfolding the matrix according to the…

A: The given matrix

Q: Show that every 2 x 2 matrix A of determinant 1 is the product of three elementary matrices. This…

A:

Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A: Consider the given matrix, The characteristic polynomial of A is |A - λI |

Q: Find the determinant of the matrix a a b a a a b a A = a baa bаа а by applying appropriate…

A: For a given matrix A, |A| is the determinant

Q: Let A be a (12x12) matrix such that the dimension of its column space is 12. Then Select all…

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A:

Q: Let P be an m × m matrix with entries in the polynomial algebra F [x]. L:1.1.

A:

Q: [A]-and (8) [: and (C]- then find (A +(8]C]

A: see below the answer

Q: The given T is a linear transformation from R2 into R². Show that T is invertible and find a formula…

A:

Q: When calculating F dr is obtained as a result: A) - 16.884 B) - 11.959 C) 11.959 D) 16.884

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Introduction: The linear transformation is invertible if and only if the corresponding matrix is…

Q: Let A be a (6x6) matrix such that the dimension of its column space is 6. Then Select all possible…

A:

Q: Let A and B denote two square matrices. Then answer the following. (a) Prove that a square matrix is…

A:

Q: Let Ao be an 5 x 5-matrix with det (40) = 3. Compute the determinant of the matrices A1, A2, A3, A4…

A:

Q: Let A be an n x n matrix and let C be the matrix of cofactors of A. Let b be a vector of length n.…

A:

Q: Let A is an orthogonal matrix, that is, AAT = I and B? = I. Compute the determinanm of the matrix…

A:

Q: Show that the determinant of the matrix B = xl – A, where I is an identity matrix and A = [1 2 01…

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A:

Q: Determine if the following statements are true or false. (a) A square matrix has an inverse if the…

A: Here,   We have given some statements about matrix now we have to determine whether they are true or…

Q: The given T is a linear transformation from R2 into R² Show that T is invertible and find a formula…

A:

Q: Let p(x) = 5x + 4x³ + 3x² + 2x + 1 and 0 1 0 0 0010 0001 0000 A = Find the matrix p(A). What is the…

A: