1 Suppose that a 3 x 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 2 |-7 4 2 Find A.

Q: 1. Give an example of a 2 x 2 matrix with no inverse ( singular). Show how it become singular 2.…

A:

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

A:

Q: Suppose that A (A, then det(B)- Select one: A. 15 OB. 5. OC -15 ODO th ) is a (4 x 4) matrix, where…

A:

Q: 6. 5 X•W Compute x using the vectors w = -2 and x =| - 2 - 3 2 (Simplify your answer. Type an…

A:

Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

Q: Given a 3 x 3 matrix in terms of a scalar c and that det(A) = 8 , find the value(s) of c if 2 -1 3 2…

A:

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

A:

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

A:

Q: Suppose A and B are invertible 1 x n matrices. Check all the true statements below. ABB÷¹A = AI„ A =…

A:

Q: 3. Find x such that the matrix A is equal to its own inverse. 2 -3 A %3D 3

A: Given :  The given matrix is   A = -2-33x To find : We have to find x such that the matrix A is…

Q: 1. Find the general solution of x =x2 – x1 + t, x, =x2. 1 2 3 2. Explain why we cannot aclculate the…

A:

Q: SKIP The 4 x 4 matrix A satisfies the matrix equation A = 3A". Find all possible values for det A.…

A: We will use the following properties : (1) det(AT) = det(A) (2) det(AB) = det(A) det(B) (3) det(c•A)…

Q: A = 1 -2 0 -3 -1 -2 0 1 3 3 -2 0 4 4 0 -1

A:

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

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: 1 4 Let A= and let B be an unknown 2×2 matrix. Calculate det B given that 1 2 det(AB)= 32.

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 be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).

A: Recall the following. If A is a n×n matrix and m be any positive scalardet k A=kndet Adet Am=det Am

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

A:

Q: 4. (a) Suppose that A and B are invertible matrices and c is a scalar. Solve the following equation…

A:

Q: A = 1 0 -1 Lo 0 -2 -3 -2 -2 1 3 3 -2 4 4 0 0 -1

A:

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: 1 2 Compute the adjoint matrix of A 3 2 2 2 3 Select one: a. -7 4 -5 7 -7 -5 3 -1 -2 %3D -7 -5 41 d.…

A: We have given a matrix and we have to find the adjoint of A.

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1 AP =…

A: A square matrix A of order 2x2 is said to be diagonalizable if there exist an invertiable matrix P…

Q: For every 3 by 3 matrix A and a scalar c, det(c A) = c det(A). True False

A: The statement isFor every 3 by 3 matrix A and a scalar c,

Q: |2 0 if A=| -3 -2 4 and B= 1 find the Matrix X such that 3A+4X=5B 1 3

A:

Q: Suppose A is an n x n matrix with A² = A. Show (I – 2A)−¹ = I — 2A.

A:

Q: 1 1 2 Q1. If [A]=3 k1where k is constant. %3D 4 2k i) For what value(s) of k the matrix A has an…

A: For Inverse to exist determinant should be non-zero.

Q: Find the matrix X, such that XDC - 2XC — ХС? + С satisfies. 3 4 4 6 6 5 C = 1 2 1 D = 1 3 -2 4 -2 -4…

A:

Q: 0 1] ¹-[i J. (we E3.2. (15) Find all 2×2 matrices B that commute with the matrix A= say that the…

A:

Q: Consider the matrix A 1 2 11 A = |1 5 0 [3 0 5/ Find the adjoint of A. b. Find the inverse of A. а.

A:

Q: Suppose that [0 1 07 R₁ E₁ 1 0 0 and A= R₂ 0 0 0 2 Ř₂ (where R₁, R₂ and R3 are the rows of the 3 x m…

A: Given E1= 010100001 E2=100010021A = R1R2R3

Q: Let M = -3 2 -3-2 M³ + c₁M² + c₂M + c3I3 = 0, where I3 is the identity 3 x 3 matrix. C1 || S || C3…

A: Here the matrix is given by M=-11-3-3232-32 Here the equation is given by M3+c1M2+c2M+c3…