Let B denote a Boolean algebra. Prove the identity va, b e B, (a · b = 0) ^ (a+ b = 1) = a = b. That is, prove the complement b is the unique element of B which satisfies (b · b = 0) ^ (b + b = 1).

Q: If B has a column of zeros, then so does BA if this product is defined. True O False 4

A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B?…

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Q: Confirm the following identity without evaluating the determinant directly a₁ b₁+ta₁ c₁ +rb₁+sa₁ a2…

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Q: Let 1 2 A = 3 6 Is A invertible? Explain your answer.

A: To verify is the given matrix A is invertible Or not.

Q: Are the following matrices invertible? Choose Choose Choose Choose ✓ 1. v2. v 3. v4. 3 [54] -40 [ 0…

A: solution are given below..

Q: What is the kernel and image of the map

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Q: Suppose I + AB is invertible. Show that I + BA is also invertible by showing that (I + BA)¯ = I –…

A: Assume that I+AB is invertible.  Then, I+ABI+AB-1=I ⋯ 1. Use equation (1) and calculate…

Q: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

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Q: Find the inverse of the following matrix: -7 5 -6 5 -2 3 1 −1 1

A: Given matrix: We have to find the inverse of the given matrix.

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: 1. Use row operations to find the inverse of '1 1 2 3 6 5 3 3 7

A: Solve for the inverse of the matrix

Q: Draw the arrow diagram for each composition of relations S and T represented by matrices: S: 101 T:…

A: The two relations S and T represented in matrix form are  S=    101            011…

Q: 1. If two Hermitian operators A and B commute, show that they can be simultaneously diagonalized.

A: Given :-  If two Hermitian operators A and B commute , then they can be simultaneously diagonalized.

Q: Find, if possible, A + B, A- B, 2A, 2A- B, and B + A = 5-6 2 3 -4 1 (a) A + B 183 11 (b) A - B 188…

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Q: What is the coefficient What is the coefficient of rx3x3 in (x₁ + x2 + x3 − x4 - x5)⁹? 1 13 of 2¹3…

A: To find the coefficient of x14 x32 x43 in (x1+x2+x3-x4-x5)9 we will use binomial theorem.  The…

Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

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Q: R^n×n is invertible, show that AB is similar to BA for all B ∈ R^n×n.

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Q: Consider a linear code with generator matrix G = Encode the message 111 110 101 010 using this code.…

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Q: Evaluate the Boolean power A3 where [1 01 A = 1 1 1 1

A: Boolean Product : Let us consider two matrices A=[aij]m x n  and  B=bijn x p be zero-one matricies.…