Let A be an nxn matrix. If A-= det A adj A is computed, what should AA be equal to in order to confirm that A has been found correctly? В I E E 3 E X, Insert Formula

Q: Let B and C be n×n matrices with the property that Bx = Cx for all x ∈ Rn. Show that B = C.

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Q: Let B be the matrix obtained from A after the row op- erations 2r3 → r3, r1 ↔ r2, 4r1 + r3 → r3, and…

A: Given: The det(B)=2 The row operations are: 2R3→R3R1↔R24R1+R3→R3-2R1+R4→R4 Let det(A) be x.

Q: Let A be an m × n matrix. Show that if x ∈ N(ATA), then Ax is in both R(A) and N(AT ).

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Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+1). %3D Which of the following is the matrix…

A: Let A=[aij] be a matrix of order 2×3This order means row =2and column=3A=a11a12a13a21a22a23According…

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: Let A be an n xn matrix, then for any r ER, det(rA)= 1 det A.

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Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 14 x 7 matrix. Then = D Check Answer

A: Given that T: R^b to R^a is defined by T(x) ° Mx and M us 14 × 7 matrix.

Q: Which of the following is an elementary matrix, E, such that EA= B for 1 %3D 1 0 1 A = 2 2 and B = 1…

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Q: e) Let A be an n x n matrix. If det(A – AIn) = 0 for some ) e R, then det(A² – X²In) 70.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let A, B and C be n x n matrices. Then (2AT + BC)T 2A-CTBT O is equal to the above 2A + CTBT is…

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Q: Let A be an nxn matrix, then for any r€ R, det(rA) = det A. Select one: O True O False

A: We have to state TRUE or FALSE for the given question.

Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 24 x 19 matrix. Then %3D a = b =

A: If T: from Rb to Ra then M is always a×b matrix.

Q: If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x =…

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Q: Find the matrix E so that EB=C, where |1 a2 az 0 B2 B3 a1 a2 dz B= b, b, b, & C= |C1 C2 C3 with a,+0…

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Q: Set up the 4 x 3 matrix E with E¡i = 0; = Vdi (the ith singular value) and all other Eij = 0.

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Q: If G = X| is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for an)- any number A. Is…

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Q: Let A, D, and P be n × n matrices satisfying AP = PD. Assume that P is nonsingular and solve this…

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Q: ve that for every matrix A, (AT)T = A

A: We have to prove that transpose of A transpose is A.

Q: (4) Given matrix A = and that h(T) = T² – 2T – 7, find h(T).

A: We use properties of matrix

Q: 11. Let A be an m x n matrix and let x, y e R". Prove that if Ax = 0 and y = ATb for some b e R",…

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Q: Let A be an nxn matrix, then for any n EZ*, det( A")= (det A)" . Select one: True False

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Q: A. For the given matrices, verify directly that (RS)* : S*R* and (EP)* = p*E* 1 3 i S = 1 0 1.R= 3i…

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Q: Given X, = [-1,0]'.do [-1,1]", go = [2,0] and G(X,)s 2. Then f(X) - f(X1) 2 ((G(X,) means the…

A: As per the question we are given : X0 = [-1  0]T , d0 = [-1  1]T , g0 = [2  0]T , ||G(X1)|| ≤ 2 And…

Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

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Q: Let A be a square invertible matrix. Which of the following is not true? Select one alternative: O A…

A: Since given A is invertible matrix, so det(A) is not equal to zero. It is always true. we also know…

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: (d) Suppose A is a 2 × 2 matrix such that for all x, y E R?, (Ax) · (Ay) = x · y Must it be true…

A: This is the problem of linear transformation.

Q: Let B be an n X n matr ix and let E be an n X n elementary matrix. Then det(EB) = (det E)(det B)

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Q: Give the value(s) of à for which the matrix A will be singular. -4 1 -2 A= 0 1 A 2 A={-2, 1} b)…

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Q: Let A be the following matrix 3 7 4 8 4 7 1 2 4, After diagonalization, P and D are found such that…

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Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

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Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+ 1). Which of the following is the matrix A?

A: A be a 2×3 matrix. This means A2×3 . entries of matrix A are ai,j=(i-1)(j+1)

Q: Apply the Gauss-Jordan method to invert the matrix given below. [1 0 0 01 1 1 0 0 1 1 0 L1 3 3 1 P =…

A: P=1000110012101331 is the given matrix to apply the Gauss-Jordan method on it that is RREF(Reduced…

Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

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Q: メ-E to to L-E 2-E to to to d-E put K-E =U E= d-fX

A: The solution to the given question is explained below.

Q: LetY∼Nn(0,Σ) and let A be any nxn symmetric matrix of rank r. Prove that Y′AY∼ χ2 if and only if…

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Q: (4) Given matrix A = ( ), and that h(T) = T² – 2T – 7, find h(T).

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Q: If a is skew symmetric nxn matrix and n is odd,prove that det A = 0.

A: Consider a skew symmetric n x n matrix A where n is odd. Here the objective is to prove that det(A)…

Q: Find an elementary matrix E that satisfies the stated equations. 8. 1 5 8 5 8. 1 5 B = 2 -7 D -6 21…

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Q: Suppose that A is an n x n matrix and det(A) = 2, det(A +I) = 3, and det(A+2I) = 5. Compute the…

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Q: * Show that if R3 of B (where B is some matrix) is replaced by R3 + R3 – 4R1 the result is EB, where…

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Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find e^t where A is the matrix A - -4 1 -1 -2 eAt +

A: Given that A=−41−1−2

Q: Which of the following is the LU-factorization of the matrix 1 0 a) Бая 0 1 0 -1] 1 1 0 b) :] 01 0 1…

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Q: Let B be a Sx5 matrix and Caa): (a-1)(X-メーい(メ) Than the rann of 21-B is? A)S B) 4 c) 3 D) can't…

A: Rank of any matrix is equal to number of non zero rows of matrix when it is in row reduced echelon…

Q: W is a 120 x 60 weight matrix, What are the dimensions of dW? According to the principle of…

A: Given that W is a 120×60 weight matrix. We have to find the dimension of dW Since, we know that…

Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

Q: Are there values of rand s for which i 0 0 r- 5 0 s-4 r+ 5 0 0 has rank 1 or 2? If so, find those…

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Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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Q: (4) Given matrix A= and that h(T) = T – 2T – 7, find h(T).

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.