Let A and B be 2x2 matrices with |4|--2, |B|= 4 . Give the value of the following. If there is not enough information for the calculation, state that. a) |4+ B| |38| b) c)

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

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Q: Show that if A is any m × n matrix, then Im A = A and AIn = A.

A: We know that if A is a matrix of order m x n and B is another matrix of order n x p, then their…

Q: If A and B are orthogonal n by n matrices, then AB is also orthogonal. True or False? Give an…

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Q: Let A, B be 2 x 2 matrices, C a 3 x 3 matrix and D a 1 × 1 matrix. Find the condition on these…

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Q: Let A be an n × n matrix and let Q and V be n × northogonal matrices. Show that ||AV ||2 = || A ||2

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Q: Let A and B be n × n nonsingular matrices. Find nonsin- gular matrices P and Q so that PAQ = B.

A: Given that A and B  are n×n non singular matrices. An n×n matrix A is non singular only if A is…

Q: Find the charo cteristica poly no nomi the matrix A = 3. 3. /- P(x) = 1.

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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: 2) Suppose that A and B are nxn matrices that satisfy AB=AB. Show that AB = AB.

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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: 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: Prove that (A + B)² = -(A + B) in matrix..

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Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

Q: Suppose that A is an m×n matrix in which no two columns are identical. Prove that A∗A is a diagonal…

A: Given that A is an m*n matrix in which no two column are identical.Since A*A is defined only if A…

Q: Suppose that A+ is a 2 × 2 matrix and that A+ = -A. Show 7.2 that iA is awesome.

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

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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: What is the only 3x3 matrix B such that for every 3x3 matrix A, ВА — 2A? What is the only 3x3 matrix…

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Q: Show that A = P-¹BP. [2-13] -4 and B = 1 -2 -2 2 are similar matrices by finding an invertible…

A: To show that          A=7-132-4, and   B=1-2-22 are similiar matrices.

Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

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

Q: linear algebra question.

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Q: Prove that, for square matrices A and B, AB = BA if and only if (A B)(A + B) = A2 - B2.

A: Given: for square matrices A and B, AB = BA if and only if (A B)(A + B) = A2 - B2.

Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

Q: Prove that if the diagonal entries of a diagonal matrix are permuted, then the resulting diagonal…

A: Permuting the diagonal entries of a diagonal matrix D amounts to permuting the rows of that matrix…

Q: A nxn matrix is called nilpotent if there exists an integer p such that AP=On. Show that each of the…

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Q: Determine which of the matrices in are symmetric. 3 4

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Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

Q: Find 2 × 2 matrices A and B such that AB = O but BA ≠ O.

A: To Find: 2 x 2 matrices A and B such that AB = O but BA is not equal to O Here O is a zero matrix…

Q: Construct a 3 × 2 nonzero matrix A such that: Ax = 0 has only the trivial solution.

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Q: Find two different 2 × 2 matrices A such that A2 = O .

A: Let A=abcd be the 2×2 matrix.

Q: Define the matrices 2, A = 1 ). B- ( ).c-( ). D - ( ) = - (;). 3 4 ‚E 4 3 1 1 2 1 В - C : 2 -4 -2…

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Q: Prove that, for square matrices A and B, AB = BA if and only if (A - B)(A + B) = A2 - B2

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Q: Suppose that Q is a matrix with the property Q−1 =QT . Show thatqij = Qij/det(Q)

A: Given: Q-1 = QT To Prove: qij = Qij/det(Q) Formula Used: If A is a square matrix, then its inverse…

Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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Q: Compute for matrix A. matA = matB x matC * [1 B = 2 [3 C -5. 4

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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: are the two matrices Simi Siari? If So find B=P'AP 20 030 3 00 A=

A: The solution are next step

Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

Q: Suppose that A and B are square matrices with the property AB = BA. Show that ABn = BnA for every…

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Q: Show that for any square matrices A and B, Tr (AB) = Tr (BA)

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Q: Determine which of the matrices in are symmetric. -6 2 2 -6 2 -6

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

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Q: Find two unequal 2 × 2 matrices A and B such that

A: The objective is to find two different 2 × 2 matrices A and B such that AB=1001 Let A=pqrs, B=tuvw…

Q: Reduce the iven into RREF, matrices and hence determine the rank of each matro. 32 1 -1 3 -6 7 1 -2…

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Q: If the n x n matrices A and B are orthogonal, which of the matrices in Exercises 5 through 11 must…

A: Given- A and B are n×n orthogonal matrices. To find- A+B is orthogonal or not?     Concept Used-…