Example 1: For the matrices A = 0. and B= compute AB andA-1 and B-1 and (AB)-1.

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

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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: 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: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

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Q: Demonstrate that A A-1 = A-1 A = I

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Q: Show that AB and BA are not equal for the given matrices.

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Q: Find the matrix product AB, if it is defined. 1 0 2 - 2 A = 0 3 B = 2 -2 2.

A: Given, A = 1003  B = 32-22-22  We have to find the product matrix AB.

Q: find A*B and B*A for the matrices A= 10 1 2 1 1 3 2 -1 B= 0 0 3 1 2 4 -1 -1 0

A: We have to find AB and BA for the matrices                                             A=10121132-1…

Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

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: Show AB + BA for the indicated matrices. A= 2 3] B = -1

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Q: Show that A and B are not similar matrices

A: Given:

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: Find the matrix product AB, if it is defined. -2 3 -2 0 A = B = 3 2 -1 1 O A. 4 0 O B. 1 3 -3 2 -8 2…

A: A = -2332B = -20-11

Q: Express A and A-1 as a product of elementary matrices. 0 5] A = 0 1 6 1 0 3] [1 0 5] 0 31

A: Here in the given question matrix A is given and objective is to express A and A-1 as  a product of…

Q: 3. Give an example of two 2 × 2 matrices A and B for which (AB)² # A²B².

A: To prove above equation with an example

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: 2 2 3. Transform the given matrix to RREF -2 1 1 -1

A: The given matrix is; 3 2 2 -2 0 1 1 -1 0. Repost the next question.

Q: Compare (AB) 1 to B 'A for the matrices below. 2 1 4 9 A = B 11 1 2

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Q: 2 if A=| -3 -2 4 and B= 1 ,find the Matrix X such that 3A+4X=5B 1 3

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Q: Find ∣A−1∣ for the matrix

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Q: Let A and B be n × n matrices. If AB = A then B is the identity matrix In. True or False

A: To write that true or false

Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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Q: Show that AB and BA are not equal for the given matrices. -2 1 8 0 A = 0 6 -1 2 АВ ВА

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Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: Let A, B, and C be invertible matrices. Then (4BT A-1C²)-1 is equal to None of the mentioned equal…

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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: Use the method of Example 6 to compute the matrix A10, where 1 0 A = -3 2

A: The given matrix is A=10-32. Observe that, A2=10-32 10-32=10-94=10-3·22-122A3=10-94…

Q: Consider the following matrix. 2 -1 1 A =-4 -1 -4 1 -1 0 Choose the correct description of A. 1 if…

A: A matrix is said to be singular if determinant of that matrix is zero otherwise the matrix is non…

Q: if A is a 3x3 matrix and det(3A^-1)=9, then det(A) is

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Q: Let A and B be n x n matrices. If AB = [0], then BA = [0]. A True False

A: Solution

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: B: find A of the matrix 2 1 3 3 2 -1 -4 3 -1

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

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Q: Show that AB and BA are not equal for the given matrices. -2 1 8 0 A = 0 5 -1 2 АВ ВА

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Q: Find if possible the matrices: a. AB   b. BA.

A: Given that: The matrices, A = -1-2-3  , B = 123

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

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Q: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

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

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Q: -1 Find the product of matrices of A = 1 and B -2 -1 3 0 2 1 -1 0

A: The given matrices are: A=-1310-2-1,B=3021-10

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

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Q: Show that AB and BA are not equal for the given matrices. 1 1 4 B = 1 1 4 4 A = 1 1 4 5 1 1 4 4

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Q: If A, B, and C are n x n invertible matrices, does the equation C-1(A + X)B¬ = In have a solution,…

A: Given A, B and C are n×n invertible matrices.

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

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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: Find an example that meets the given specifications. 3 x 3 matrices A and B such that AB ± BA 0 0 0…

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Q: Find the product of the matrices shown below. 1 3 2 1 4 A = X 1 1 2 1 1 1

A: Given product, A=132214012101×211

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

A: Two matrices are similar if they have same Eigen value  A=100020003 Find the Eigen value of A…

Q: Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0 0 1 1 1 3 • A8 = I3; and…

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