If A and B are 3 x 3 matrices, det (A) = 3, det (B) = -2, then det(AB) = det (2A) = det (AT B³) = det (A²B-¹) = det (2ABTA ¹) 1

Q: If A and B are 3 x 3 matrices, det(A) = 3, det(B) = -6, then det(AB) = det(2A) = %3D det(A") =…

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Q: (a) Show that the following statement is false: "If A and B are n × n matrices then (A + B)² = A² +…

A: The rectangular arrangement of numbers is called the matrix and the number in a matrix are called…

Q: If A is 4x4 matrix with det(A)=10, find det (24-¹A), det (A²).

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Q: If A is a 3x3 matrix and det(A) = 7, what is det(2A)?

A: Solution :-  Given : A is a 3×3 matrix               And det(A) =7

Q: Use LU decomposition to determine the matrix inverse for the following system 10х, + 2х, — хз%3D27…

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Q: 2 4 If A 1 4 - [3³] and B = [2 56 [4 2 24 find matrix such that 2A + B + 4X=0

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Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: The 3 × 3 matrix B satisfies the equation B^3 = −B. Show that B cannot have an inverse

A: We proved that, the matrix B cannot have an inverse if it satisfies the equation…

Q: solve by finding an inverse matrix 2x+y=6 x+2y+z=12 x-y-z=-5

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Q: Two matrices A and B and two numbers c and d are given. Compute the matrix CA A = CA + dB = 6 -4 9 4…

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Q: compute the indicated matrices A + 2D

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Q: For any two 3 x 3 matrices A and B, we have (А + B)(А — В) — А? — АВ + ВА - В?

A: Given statement: For any two 3×3 matrices A and B, we have

Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: X1 + 3x2 – 2x3 + 2xs = 0 2x, + 6x2 – 5x3 – 2xg+4x5 – 3x6 = -1 X3 + 5x4 + 3x, = 1 x + 3x2 + 4x4 + 2xs…

A: Given that the system of linear equations is…

Q: If possible, compute the following. If an answer does not exist, enter DNE. (A+B) + C = + A+ (B+ C)…

A: We have to solve the addition form of Matrix.

Q: If A and B are 2 x 2 matrices, det(A) = -2, det (B) = 7, then det (AB) = det (2A) = det (AT B³) = ₁…

A: We use determinnant properties (i) det(AB)=(det(A))(det(B)(ii) det(KA)= , Here k is constant and n…

Q: Given the matrices: 2-1 0 A - (²29). B- (1¹³). (7³), 0- -1 3 Compute each of the following, if they…

A: We are given the matrices A,B and C.

Q: Consider the two matrices: 2 4 1 -5 A = B = 2 Compute A + 3 B. The result is equal to: Select one:…

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Q: (1) Let A and B be two 2 × 2 matrices. Does det(A – B) = det(A) – det(B), explain your answer.

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Q: If A and B are 4 x 4 matrices, det(A) = 1, det(B) = 4, then det (AB) = det (-3A) = det (AT) = det…

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Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: For n × n matrices A and B , when does (A + B )(A − B ) = A 2 − B 2?

A: Commutative rule: The product of two matrix does not follow commutative rule: AB≠BA Given:…

Q: [2 2 Give two different matrices B so that in each case B 2 2

A: Given matrix

Q: For the two 3 x 3 matrices A and B with det(A) = -3 and det(B) = 2, Select one: O True O False det…

A: Given :mx+3y-z=m    2x+z=1              -2x-3y+mz=0  detA=-3detB=2

Q: Given 2. A and B = ( 4 Find the matrix represented by: (iii) 3(A – 4B) (iv) B+ 3AT

A: The given matrices are A=254-2  and B=-1724. (iii) Evaluate 3(A-4B) as follows.…

Q: en the definition tr rices (no numbers). (d) = a + d show that tr(A B) = tr(BA) using gen

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Q: Write equations z + 2y + 3: = a, y – z - b, and 2y + 2: - c, as the matrix equation ()-) A and then:…

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Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: If A and B are 2 x 2 matrices, det (A) = 3, det (B) = 4, then det (AB) = = det (-2A) = det (AT) det…

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Q: 2] find 1 -1 3 - If A = and B 1 |3| -2 (а) ЗА — В. - (b) The matrix X such that 3A – B+ 3X = 0. ||…

A: As per guideline we have to solve only three parts

Q: Which of the following statements is (are) true if B is a basis for the vector space V ○ (a) In some…

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