In general, matrix multiplication is not commutative (i.e., AB = BA). However, in certain special cases the commutative property does hold. Show that (a) if D1 and D2 are n × n diagonal matrices, then D1D2 = D2D1. (b) if A is an n × n matrix and B = a0I + a1A + a2A2 +· · ·+akAk where a0, a1, . . . , ak are scalars, then AB = BA

Q: If matrix A is 2 x 5 and the product AB is 2 x 4, then what is the order (or size) of B?

A: is a  matrix is  matrix.We have to find the order of

Q: Determine whether or not the following statement is true: If A and B are 2 x 2 matrices, then (A+B)²…

A:

Q: 3: For the matrices, A = [1 and B = 01 -31 (a). Show that, (A+ B)" AT +B". (b), Show that, (AB)-1 =…

A: Show that  a) (A+B)T= AT +BT  b) (AB)-1= B-1A-1  For the matrix A and B .

Q: 31. If A and B are n x n matrices, then the diagonal entries of the product matrix AB are…

A: Matrix multiplication is possible only when the number of columns of first matrix are equal to the…

Q: If A is a 3x3 matrix and det(A) = 7, what is det(2A)?

A: Solution :-  Given : A is a 3×3 matrix               And det(A) =7

Q: Consider the matrices 4 2 1] 5 4 B = 2 2 3 1 A = X = -3 0 1 2 0 8 Which of the following matrix…

A: We have  Matrix multiplication AB defined only if Number of columns of A = Number of rows of B

Q: I cant understand what's going on. can this be explained with matrices?

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Q: 3 0 A =|-3 7] 1 -1 2 4 91

A:

Q: Let A, B, C and D be square invertible matrices, such that AB = CD. Find an expression for B-¹?…

A: Use the properties of invertible matrices and their product to solve this problem as in next step.

Q: a) Find the inverse of the square matrix B: [2-4 B = 3 -1 7 0

A: The inverse of the matrix is given below :

Q: Let A and B be 2 × 2 matrices. The equation (A – B)(A+B) = A² – B² is correct. (A True B False

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Q: If A is a 1 x 2 matrix and the sum A + B can be computed, what is the dimension of B? X

A:

Q: If A, J, K, Y, and Z are all invertible square 10 × 10 matrices, solve the equation for matrix Z.…

A:

Q: Question 6 Prior to running the Boston Marathon, a runner's personal best pace for a race is 10…

A: Given that Prior to running the Boston Marathon, a runner’s personal best pace for a race is 10…

Q: The adjoint of zero square matrix is zero matrix and the adjoint of identity matrix is identity…

A:

Q: IFagx3 matrix and its inverse are multiplied together write the product. A. 00 1 0 00 B. 0 10 000

A:

Q: If A is a 2 × 3 matrix, and B is a 3 × 4 matrix, how many columns does AB have?

A: Given that  If A is a 2 × 3 matrix, and B is a 3 × 4 matrix To find how many columns does AB have

Q: Explain if the statement is true or false, and why

A:

Q: Consider the matrices A, B, C. 1 4 2 --1 3 3 -1 3 A =|3 0 1 B = C = 2 6 8 0 5 6 -1 5 7 2 a. Find the…

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Q: If A is a 3 x 5 matrix, B is a 5 x 7 matrix, C is a 7 x 11 matrix and D is a 5 x 7 matrix, which ONE…

A: ACB=A3×5 ×C7×11 × B5×7  , here the number of columns of A and the number of rows of B does not…

Q: If A and B are m × n matrices and C is an n × p matrix, then (A + B)C = AB + BC. TRUE OR FALSE

A: Here we define true false for matrix multiplication.

Q: The product of a 2 ´ 3 matrix and a 3 ´ 2 matrix is

A: When we do multiplication: The number of columns of the 1st matrix must equal the number of rows…

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: Show that A = P-¹ = 2 -1 -5 2 -2 -2 0 1 -4 and B = 3 6 -8 2 2 -4 , P = 4 6 are similar matrices by…

A: Given: and To show: and  are similar matrices by finding an invertible matrix  satisfying

Q: The formula (IMG) is true for matrices. Select one: A) True B) False

A: From the given problem: A+BA-B=A2-B2 As we know that, in matrices:  matrix AB≠matrix BA

Q: Determine 3B  if the matrix is    1        5                                                   -4…

A: the matrix B is 15-48 we have to find the value of 3B.   as we know that if we have a matrix A as…

Q: If AB is a 4 x 2 matrix and B is a 1 × 2 matrix, then the size of matrix A is

A: We can multiply two matrices only when the number of column in the first matrix must be equal to…

Q: If A and B are square matrices of the same size, is (A + B)2 = A2 + 2AB + B2?

A: In matrices, the commutative properties are not valid. That is order of the matrices multiplication…

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.