3. Given A and B are 3x3 matrices with det A = -2 and det B = 3 compute the following and show what property you are using directly in your work: a) det AB b) det A c) det AT d) det B-1

Q: If A and B are sk ew-symmetric 2 X 2 matrices, under what conditions is AB skew-symmetric?

A:

Q: Consider the two matrices: 4 -5 1 B = A = -6 -3 Compute A +3B. The result is equal to:

A: GivenA=24-60 B=1-5-32To compute12A+3B

Q: If A and B are 3 x 3 matrices, det(A) = 3, det(B) = -6, then det(AB) = det(2A) = %3D det(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: 4. If det(Adj(A)) = then what is det (A-1) if A is a (4 × 4) matrix?

A:

Q: Suppose A, B and C are 2 × 2 matrices with det(A) = 3, det(B) = -2, and det(C) = 2. Find…

A: NOTE: Refresh your page if you can't see any equations. . properties of a determinant are where…

Q: 2 3 uppose A = = B+C where B is symmetric and Cis skew-symmetric 5 6 b bi2 b12 b2 matrices, B = then…

A:

Q: 3 1 come up with two matrices D and C such that DA CA but D (b) For A C. 6 2

A: The given matric,

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.…

A:

Q: If A, B, and C are 3×3 matrices; and det(A) = 1, det(B) =-1, and det(C) = 3 then compute:…

A:

Q: If A, B, and C are 3×3 matrices; and det(A) = 5, det(B) = −2, and det(C) = 3 then compute: det…

A:

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det(A² BC-1)?

A: Given A, B and C are 3×3 matrices. and A=-3,B=-2,C=6 Find the determinant of A2BC-1.

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

A:

Q: If A, B, and C are 5×5, 5×2, and 2×9 matrices respectively, determine which of the following…

A: if  A    be a matrix of order  m×n    and  B be a matrix of order p×qthen product  of matrix AB is…

Q: Show that for 2 × 2 matrices A & B the following equation holds. det(A + B)? = [det(A + B)]² Without…

A: a) Show that for 2x2 matrices A and B the following equations hold               det(A+B)2=det(A+B)2…

Q: Show that these four matrices form a representation of the Vierergruppe, whose multi- plication…

A: 17.2.2 We have to show that given matrices  I,A,B and C form a Vierergruppe. Concept:…

Q: Let A be a 4 x 4 matrix with det(A) = −10. 1. If the matrix B is obtained from A by adding 7 times…

A: Given A be a 4×4 matrix with detA=-10

Q: Suppose that both A, B ore 2x2 matrices such that det (A) = 2, det (B)=6. Then det (AB) = %3D det…

A: As per our guidelines only 3 sub-parts can be solved: Solving 1st three sub parts in the steps…

Q: Suppose A and B are 3x3 matrices with det A = 2 and det B = -3. Find det(2BTA-B).

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Q: Let A, B, C be (3 x 3) matrices, such that det(A) = 2, det(B) = 7, det(C) = 1. What is the value of…

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Q: Consider the following 2x2 diagnal matricies k  0 0  j If k, j are subsets of {1,2,3,4.....9} how…

A: We have 9 choices to fill place of k.  Also we have 9 choice to fill place of j.

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)

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: Suppose A , B and X are matrices such that AX - A = B, where 1 -1 3 4 1 20 4 5 6 -5 1 2 1 -2 1 A = 3…

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

A:

Q: If A, B, and C are 3×3 matrices; and det(A) = -1, det(B) = 4, and det(C) = 3 then compute:…

A: We know properties of determinant for n×n matrices A, B…

Q: If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and…

A: Given matrix B arises from a matrix A by elementary row operation. We have to find the relationship…

Q: If A, B, and C are 4x4 matrices; and det(A) = 4, det(B) = 2, and det(C) = -1 then compute:…

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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

Q: Show that if A and B are n × n matrices and N(A − B) = Rn then A = B.

A:

Q: If a 4 by 4 matrix has det A = ½, find det(2A) and det(-A) and det(A2) and det(A-1 ).

A: Now,

Q: 1. For any 3x3 matrices A & B: Verify that (AB)" = B"A". %3D

A: By using the properties

Q: If A and B are 3 × 3 matrices and detA=2 and det B = 4, find det (5A* BTΑ-)

A: See the details solution in below

Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: 7. If a n x n matrix B is obtained from A, using only m number of row interchanges, then det A det B…

A:

Q: If A, B are 3 x 3 matrices such that det(AB)-1)% = det(adj(A)) = 25. Then det(3A". (B)-') 20 and O…

A: We are given that A and B are 3x3 matrices. We are also given that detAB-1=120 and detadj(A)=25.…

Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: (b) Write the three matrices that are used in Cramer's rule to compute the numerator of the…

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Q: If A, B are 3 x 3 matrices such that det(AB 1) = 12 and det(adj(A)) = 16. Then det(3A". (B)1) %3D

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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: If A and B are nXn matrices, then (AB)²=A²B? A True

A:

Q: If A, B are 3 x 3 matrices such that det(AB)-1)= and 20 det(adj(A)) = 25. Then det (3AT. (B)-1) a.…

A:

Q: 6. If A, B,C and D are 3 x 3 matrices with det(A) = 2, det(B) = 4, det(C) = 3 and det(D) = -2, find…

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Q: 6. Suppose A and B are 4 x 4 matrices where |A| = and |B| = 3, compute: (a) det (24)~!) (b) det…

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Q: 1. If A is 3x3 matrix with det(A) = 5 then det(3A) %3D O 3(5)=15 9(5)= 45 O 27(5)= 135 5(5)(5)= 125

A:

Q: If A, B are 3 x 3 matrices such that det(AB-1) = 12 and det(adj(A)) = 16. Then det(3A". (B)1) %3D O…

A: Consider the given expression, det3AT·B-1 It is given that detAB-1=12 and detadjA=16. now, use the…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.