2. Let a, b be non-zero real numbers. Let T be an n × n matrix. If T satisfies (Tal₁)(T - bln) = Onn show that 1 T-¹=(-T+(a + b)In). ab In your proof, you must explicitly state any properties or theorems you have used.

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: matrix P and a matrix C of the form -21 a -b b ces P and Care mma to separate answers as needed.) no…

A: Let    Given that Eigenvalues of A are 5+2I and 5-2i With corresponding eigenvectors are 2+2i-i And…

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: 04) X = [ Y = ; Hand Z = [ 3 Q.4) X Prove the Distributive laws of multiplication over Subtraction…

A: The given matrices are X=23-10,Y=0131  and  Z=22-10. The distributive law of multiplication over…

Q: Show that the matrix X -1 : -1 -1 X : 0 : : X is Positive Definite if x > √n −1 The lower right…

A: The given matrix is An=x-1...-1-1x00::⋱:-100x. To Prove: This matrix is positive definite if…

Q: Answer all the questions: (2 1 1 1. The characteristic polynomial of the matrix 0 1 0) is A1 1 2. a)…

A: Here the given matrix is                                        211010112 We have to find the…

Q: For A 3 1 N² = A. 2 find a 3 x 3 matrix X such that

A:

Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

A:

Q: We call g(x1, x₂) = ax² + 2bx1x2 + cx a quadratic form, a, b, c are constants. Suppose X1 X = try to…

A:

Q: Зх — Зу — 6z %3D —3 2х — 2у — 4z %3D 10 2х + Зу + z %3D7 -

A: Given system of equations, 3 x-3 y-6 z=-32 x-2 y-4 z=102 x+3 y+z=7 The objective is to solve the…

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: Which of the following statements is correct for any 5 x 5 matrix A? Select one: None of them The…

A: To find the correct value of entry 54 of adj(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: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

A:

Q: uninfected lightly infected highly infected column sum eaten by birds 1 10 37 48 not eaten by birds…

A: Chi square test for independence is used to test the association between the two variables.

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: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

A:

Q: Which of the following statements is/are correct? Please select one or more: For every matrix A,…

A:

Q: O Let (e>+) is aring of complex numbers and Mz be aringof2 matrices aud g e-ɔM, desined as Follows:-…

A:

Q: Give an example of a non-zero 2 × 2 matrix R which satisfics R² = 0. Suppose that M is an n x n…

A:

Q: 9. Show that the matrices (6) 65), (8), and (1) generate M2×2(F).

A: We have to show that the matrix  and  generate

Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: 6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k…

A:

Q: Which do you find easier? 3 1 (₁ - ( ) -- (3) (a) A = B = -1 1 1₁- (b) A = ()--(²3) B = -2 15 2 2-2

A:

Q: For each of the following statements, indicate whether it is true or false. 2. justification is…

A:

Q: For each of the following statements, indicate whether it is true or false. 2. justification is…

A: We will use property of rank here to justify the statements.

Q: Find the matrix of the quadratic form. Assume x is in R². 9x² - 12x₁x₂ + 8x²2 b. 8x² +10x₁x2

A: The quadratic form:a) b)  To Find:Matrix of quadratic form.

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 that there does not exist a 43 × 30 matrix with entries from {0, 1} such that there are 17 is…

A: As per the Guidelines, we can solve only one question. Please repost it for the other part.We can…

Q: If Y = X(XTX)-¹XT where X is a square matrix and (XTX)¹ exists, then: Statement I: Y is a square…

A: Statement I :Suppose  is a    matrix.Here,                        ( since )               (By…