Q.1 Consider the following matrix (-1 3 0Y A = 2 0 2 2 1 4 1 B- 2 -1 5 -3 0 1 10 C-2 A. Show that a. (A')' - (4"')"

Q: [2 1 -2 17.- Define and prove the range of the following 3x4 matrix: A = 4 4 2 7 -3 1 18

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: 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: 21

A:

Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

A:

Q: 3 21 3. The all values of a and B, so that the matrix 4-3 1 4 is positive definite, are [2 B 2] (b)…

A:

Q: ^ - [ 3 ] and B = [² = 4 5 If A 4 5 7 6 find 3A-2B+ I where I is a unit matrix.

A:

Q: .

A:

Q: A B Which of the following is the solution for 關 EXO- = 台 = -5/2 3/2] 2-5/2 of the matrix equation…

A:

Q: -3 -2 -3 17. Find the inverse of the matrix A= 5 3 5 2 1 1

A: Given A=-3-2-3535211 The inverse of A is given by A-1=1Aadj A A=-3(3-5)-(-2)(5-10)-3(5-6)…

Q: 4. In fitting a straight line, the formula to find the sum of the squares of the residuals is (a) E…

A: 4. Hint: Here we need to just write the sum of the squares of the residuals.

Q: 2 1 4 6 Find a matrix X that satisfies A(X+I,)=B, where A = and B = 6 5 3 5

A:

Q: 1. (C"B)A" 3 A = -1 B = -1 4 C = 1 2. tr(4ET – D) 1 1 1 2 6. 1 3 D = -1 1 E = -1 1 3 2 4 4. 3

A: To evaluate the given matrices.

Q: 2. Consider the four matrices, 1 2 1 2 3 C = 4 5 6 1 2 3 4 3 A = 5 6 3 4 5 6 78 9 Solve for: а. АВ…

A:

Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: (1) If a matrix A has 10 columns with nullity(A) = 5 and nullity(A) - 3, then A has 7 rows? (i) If A…

A:

Q: 4. For each of the following conditions, construct a 3 x 3 matrix the given properties. (a) dim…

A: Nullity of the matrix

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: Note: m=0 + m -2 6. 1. Let 1=* = l and C = |14 — т аnd C — 3 18 + m -10 -21 Find the matrix X, if A?…

A:

Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

Q: 1. If 1+ A is nonsingular, show that (I+ A)"' and I– A commute and (I + A) +(I+ A')"=1, where I is…

A: Given I+A is nonsingular and we have to show that I+A-1 and I-A commute and  I+A-1+I+A-1-1=I

Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

A:

Q: 1 0 (¹²2₁) 1 1 of the matrix B x A? Let A = 00 01 02 03 O-1 O-2 O-3 and B = 2 1 (GD -1 0 1 What is…

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: 3 x 3. Find A² - 5A + 4I3, if A = -2 1 0 -1 43 0 85 where I3 is a unit matrix of order

A:

Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

A: Introduction: If the transpose of a square matrix with real numbers or elements equals the inverse…

Q: Find the transpose of the matrix. -2 -1 D = 1 4 -3

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: 1. Write down the 3 × 2 matrix A with aij 2ij – cos 3

A:

Q: 2 - P=[1] and o-[11] 41 Q = Find a 2 x 2 matrix X such that PXQ= = -4 27

A: