Let A find on Conditions a,bic and d has infinitely that AX =o many solution . what must there Pere be true about a,b,c and d in order for A to be invertible ?

Q: 4 Let A b [² }] Find Conditions on 1 c d a,b,c and d that AX =0 that AX=0 has infinitely many…

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Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

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: Let A ∈ M (3,R) be invertible and C, D ∈ M (3,2,R) . Solving B from the equality A(B+Ct)t = D, what…

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Q: Find all solutions of the system of congrucences солу da st 8x + 5y = 1 (mod 13) 4x + 3y = 3 (mod…

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Q: 1.1) If A is invertible, then adj(A) must also be invertible. True or false

A: We can find the answer as given below.

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

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Q: 21. Find all numbers r such that [242] 1r 3 112 is invertible.

A: Given matrix is .We have to determine all values of  such that the above matrix is invertible.

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

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Q: Suppose (B - C) D = 0, where B & C are m x n matricies and D is invertible. Show that B = C.

A: Given that  (B-C)D =0 here B and C are m×n matrices

Q: Let M-{1, 2}. Then O IP(MxM)=4 None of the mentioned O MxM={1, 4} O MxM={(1,1),.(2,2)} O IP(M×M)|=16

A: It is a set and relation problem

Q: 45. Use the function fbelow to determine each limit: f(x): - A. lim f(x) x → B. lim f(x) x→-3- -2x…

A: The given function is f(x)=-2x/(x+3)2Find the limit. Find the right hand limit and left hand limit.

Q: 1 a 0 b 1 -1) 31 For which values of a and b is-2 invertible? Why?

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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Q2\ Prove that Ax (B+C) = A×B + AxC When A= 2i + j-k B=i-j+ 2k Sumer C=i+2j+k

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Q: If both z + w and zw are real, how to prove that either z = w (conjugate) or Im(z) = Im(w) = 0?

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Q: One of the following is always true A) If det(A) = det(B), then det(A+ B) = 2det(A) B) adj(AB) =…

A: Solution

Q: Suppose Ax = b and Ay = b* are both solvable. Then Az = b + b* is solvable. What is z? This…

A: It is given that Ax=b and Ay=b* are both solvable. This implies that b and b* are in the column…

Q: Matrices A and B are row equivalent. Choose one mathematical statement that can be made concerning…

A: Given that, The matrix A and B are row equivalent. A is invertible because A has four pivot points A…

Q: Let a ER and let: 1 -2 2 1 = (1 ) A 1+ a 4+a -2-a a a You may assume without calculation that chÃ(x)…

A: Kindly refer to Step 2 for the solution.

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1,…

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Q: 4. Suppose A, B, C € M₂ (R) and C is invertible. If AC = CB, must A = B? Give a proof or a…

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