If A and B are symmetric matrices (AT = A, BT = B), which of the followw- ing is not necessarily symmetric? (A) -4BT (В) А + B (С) АВ (D) AT A O A O B O D

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

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

A:

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: If A and B are n × n diagonal matrices, show that AB = BA.

A:

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: Due to what property, applied to the matrices below, do we know that A + B = B + A?

A: Due to Commutative Property Of Addition of matrices, we can say that: A+B=B+A. Where, A,B,C are…

Q: Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

A: See the attachment

Q: Let A and B be n × n matrices. Show that if AB is nonsingular, then A and B must be nonsingular.

A: Matrix: Let Ab is nonsingular. Therefore ABx=0 has only the trivial solution. Now let b be singular…

Q: If A and B are matrices 3 x 3 order with 12A| = -1 and |2B³| = 16, then calculate |A-1B"|.

A: Here, A and B both are of the order 3×3. So, A-1 and BT are of the order 3×3. Now, from the…

Q: Let A, B, and C be three nonzero n × n matrices such that AC = BC. Does it follow that A = B? If so,…

A:

Q: Prove that if A and B are similar matrices, then ∣A∣ = ∣B∣. Is the converse true?

A:

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…

A:

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: If A and B are invertible matrices, show that AB and BA are similar.

A:

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: What is the difference of matrices M=(-1,0,2)(0,-3,1) and N=(0,1,2)(0,0,-3)?

A:

Q: If A and B are square matrices of the same size such that AB = BA, prove that (AB)2 = A2B2.  By…

A:

Q: If A and B are square matrices of the same size, then it is always the case that AB=BA.

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let A2x3, B2x3, C2x2, E3x2, be matrices. Which of the following cannot be calculated?

A:

Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: If A and B are symmetric matrices of the same order, then show that ABis symmetric if and only if A…

A: Given that, A and B are symmetric matrices.

Q: If A and B are row-equivalent matrices, then they must have the same rank. True False

A: Our guidelines for multiple questions, answer only first question  Answer = (8)  If matrices "A"…

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 and B are n x n symmetric matrices, then AB is symmetric. ... (A) True B) False

A:

Q: Are the two matrices similar? If so, find a matrix P such that B = P-'AP. (If not possible, enter…

A:

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

A:

Q: If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.

A: If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.

Q: If A and B are n x n matrices, and vector v is in the image of both A and B, then i must be in the…

A: True or false.

Q: If AB + BA is defined, then A and B are square matrices of the same size. True False

A: Given AB + BA is defined.

Q: If A, B are symmetric matrices and AB-BA, then AB is also symmetric. Select one: True False

A: Suppose A is a square matrix. Then A is symmetric matrix if A'=A, where A'is transpose of A.

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

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: Find three 2 × 2 matrices, A, B, and C such that AB = AC with B = C and A = O.

A: Consider the matrices A=0000,  B=1234  and  C=1234. Clearly, B = C and A = O.

Q: True or False If A and B are n × n lower triangular matrices, then AB is also lower triangular

A: Given, A and B are n×n lower triangular matrices. Consider 2×2 lower triangular matrix A=a0bc…

Q: Let A, B, C be n x n matrices. Show that if A is similar to B and B is similar to C, then A is…

A:

Q: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

A:

Q: Are the two matrices similar? If so, find a matrix P such that B-P-AP. (If not possible, enter…

A:

Q: For matrices A, B, and C, if A is invertible and AB-C, then True False B = CA-¹.

A:

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

A:

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

A:

Q: . We can add (or subtract) two matrices only if they have thesame .

A:

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…

A:

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: If A and B are nxn matrices, then (AB)²=A²B²_ A) True B) False

A: Solution

Q: If A and B are invertible 2 × 2 matrices with nonnegative entries, then A + B must also be…

A: Let's take one counter example of the given conditions. That is A and B are invertible 2*2 matrices…

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.