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

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Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

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Q: (iv). Find det(A¯1) of the following matrix: 1 3 -1 2 1

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Q: Consider the following 2 × 2 matrix A. 9 A = 2 = A. Determine the values of x and y for which A² x =…

A: Step 1:Step 2: Step 3: Step 4:

Q: - 1212 31 Find the inverse of matrix A using the equation A² - 5A - 21 = 0 where A = ¹2

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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

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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: * For the matrix A, find det A 1. A = = | 3 -2 1 [2 |1 -1. det A = 25 O det A = -2 O det A = 1 O det…

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Q: A frm manufactures three products, P1, P2 and P3, which it sells to two customers, C1 and C2. The…

A: a) AB Given A = 679212, B = 100500200T AB = 679212100500200T= 679212100500200= 6*100…

Q: Assume the following matrix is given Be when x = I I I X 1000 000 1 00 1 0 where x is any non-zero R…

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

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Q: Evaluate the minor and cofactor using the matrix A. 90 1 8 A = -2 2 3 00 7 minor M13 = cofactor A13…

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Q: ( ). For matrix A = if f(X) = (X+ 2)(X – 2), calculate f(A)? -16 33 17 (17 48' В. 16 33. A. -48 -48)…

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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)…

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Q: 1. b) Find the Inverse of the matrix 1 2. 1 using Gauss-Jordan method. 1 1. 2]

A: Augment the given matrix with identity matrix. Apply row operations to convert given matrix into…

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

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Q: Given the following vector X, find a non-zero square matrix A such that AX-0: You can resize a…

A: Definition used -          Product of two matrices -         The product of two matrices is…

Q: 1. For the given matrix A and vector b, 1 A = -2 2 1 0 2 -1 == 4 -2 compute the following…

A: As per our bartleby guidelines we can do only three subparts and rest part can be reposted.

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: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

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Q: 1(a) Two 3x3 matrices A, B satisfy the relation: A BA=6A+BA. Given: [1/3 A = 1/4 1/7 Find matrix B.…

A: Here we have det (A^-1) = 1/84. So A is invertible and A^-1 exists. Now A^-1*B*A = 6*A + B*A    Or,…

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

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Q: 9. Solve Assignment 3.1 #40. A = [²₁₂2] 4. Let A b. Confirm that (A-31)(A-1) = 0, where I is the 2 x…

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Q: Q1. Suppose that A and B are positive definite n x n matrices. Which of the following matrices must…

A: ACCORDING TO COMPANY GUIDELINES, WE ARE ALLOWED TO SOLVE ONLY ONE QUESTION WHEN MULTIPLE QUESTIONS…

Q: 6. Evaluate the determinant for the following matrix: O A.8 OB.-2 O C.5 O D.4 3-5 1

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Q: Q4) For Matrix A = 2 1 2 5 -1 4 1 -1, Find the following: 1 1. The Determinant of A. 2. The Minor of…

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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?…

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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: 10. Given that A and B are square matrices of order 3. If |A| = 3 and |B|= 1 then A. 2A 4B| = (-4)23…

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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: Using the matrices. [1 0 1 R1 = 0 1 1 li o 1 [1 1 1] R2= 1 0 1 li 1 Find the matrix that represents…

A: Use the given matrices.

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

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Q: (12) Use the adjoint of matrix to find the third row fourth column element of the inverse of -1 1 4)…

A: Consider the given matrix as A=0-11432-21040110-11. The inverse of the matrix A is given by…

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

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