Let A, B and C be matrices of type 2 x 3,3 x 2 and 2 x 2 respectively, such that det(AB) = -3 and det (C) = 4. Then which of the following is the value of the det [(2AB)"C=']¯? (a) -6 (b) 12 (c) ! (d) 궁 (e) -12

Q: Let A, B, C be n x n matrices. Verify that (a) A is similar to A. (b) If A is similar to B and B is…

A: Given A, B, C be n × n matrices

Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

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Q: (0) Construct two non-zero 3x3 matrices A and B such that for A its rank is greater than its nullity…

A: two non-zero 3×3 matrices A and B such that for A its rank is greater than its nullityand for B…

Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

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Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

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Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B) Upload an image or PDF of…

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Q: TRUE OR FALSE. The product of two m × n matrices is defined.

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Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

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

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Q: 3. If A, B and C are matrices with orders, 3 X 3, 2 X 3 and 4 X 2, respectively, which of the…

A: Note: There are many subparts in the question. So I will answer the first three subparts.…

Q: Consider again 2 × 2 diagonal matrices: k 0 0 j If k, j ∈ {0, 1, 2, 3, ..., 9}, how many possible…

A: Given 2×2 diagonal matrix k00j k, j ∈0, 1, 2, 3, ..., 9

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Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A" A-1)?

A: Given that A,B and C are 3*3 matrices. To find det(A^TA^-1)

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A: we have given A and B are orthogonal matrices.  We have to show that the following

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A: To write that true or false

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Q: Let A and B be two 4x4 matrices with rank(A)<4. Then rank(AB)=4. E ((C Select one: OTrue OFalse

A: We know that  Rank(AB) = min{rank A, rank B} Since Rank A &lt; 4

Q: Let A and B be two 4 × 4 matrices with rank(A)<4. Then rank(A²B)<4. Select one: O True O False

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Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

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Q: 6.- For the matrices [A] g 3 -2 4 -2; [A] =-5 3 3 2 3

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Q: Consider the matrix below A= 3 -2 4 0 -6 7 a 1 2 -2 1 -3 -4 3 1 2 Find the minor and cofactor of a

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Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: Let A and B be matrices with size 3 x 3. If only one of these matrices are diagonalizable and if…

A: Given, A and B be matrices with size 3×3det(A-λI3)=(λ-2)(λ2-9)det(B-λI3)=(λ-3)2(λ+2)(a) Eigenvalues…

Q: If AT = A-1, where A is a real matrix, then A is

A: When transpose of A equal inverse of A , then A is

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

A: To solve this problem, we use the standard result of matrix

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

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Q: Let A, B, C and D be invertible n xn matrices with n> 7, which satisfy the equation ABCT DBA"C = ABT…

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Q: 3 -1 0 2 4 N O

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Q: Let A and B square matrices where detA=4 and detB=12. What is det(A-1B)?

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Q: 17 - Which of the equations given below on the multiplyability of the matrices shown with their…

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Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: If A is what a matrix satis fying A3= A about det A7 %3D can you say

A: We have to find determinants

Q: 3. Find the inverse of the matrix A = 1 0 -2 2 4] 1 3 2, if it exists. 5

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Q: 3. Verify that the following statement is true for these matrices: (XY)-1 = Y-!X-!. A suggestion:…

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