If A is a 5 x 5 square matrix such that At = Is, then rank (A) %3D ................ a) 2 b) 3 c) 4 d) 5

Q: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix, a. Is GH defined? If so, what is the order…

A: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix,a. Is GH defined? If so, what is the order of…

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 0, a2 = 2, a33 = 5, a21 = 3, a31 = 4, and…

A: a symmetric matrix is a square matrix that is equal to its transpose.

Q: If A is a square matrix such that A2 = A, then (I-A)+A is equal to (A) (В) (C) I- A (D) I+ A

A: A is a square matrix such that: A2=A Now: (I-A)3 + A=(I-A)2(I-A)+A =(I2-2AI+A2)(I-A)+A = (I-2A + A)…

Q: Given the matrix 2 2 3 1 2 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: Given a 3 x 3 matrix in terms of a scalar c and that det(A) = 8 , find the value(s) of c if 2 -1 3 2…

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Q: snip

A: Given, A=abcdD=ad-bc≠0

Q: If A is any matrix, to what is tr (AA T) equal?

A: Let A=[aij] be n X n matrix. Then  AT=[a'ij] where a'ij=aji Let C=AAT=[cij] , where

Q: 2. Show that if A is an n x n real symmetric matrix then (Ax) y = x (Ay) for all x, y E R".

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Q: Prove that if A is an n X n matrix, then A - Ar is skew-symmetric

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Q: Given the matrix 2 2 2 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

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Q: [d, 0 D =|0 d2 0 , and vector i = d3]

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Q: sum

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Q: Let A be a nonsingular n × n matrix and let B be an n×r matrix. Show that the reduced row echelon…

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Q: Which of the following is the LU-factorization of the matrix a) 1 b) 0 1 1 c) d)

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Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

Q: If A is a nonzero matrix of the form P, then Rank(A) = 2. а

A: Let A be a n×n matrix . If Determinant of A is not ZERO, Then   Rank(A)=n

Q: Prove that for any square matrix A, ||A||3 E ||A* A||2.

A: For any square matrix A Required to prove A22 <=A*A Let, us consider the matrix, A=2314

Q: Determine the dimensions of Nul A, Col A, and Row A for the given matrix. A 0 1

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Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

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Q: Suppose A is a symmetric matrix. (Au)" : u"A

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Q: Let A = diagonalizable matrix( A = XDX-1), then X and D are: LO H O4

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Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

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

A: Since A is a skew-symmetric matrix we have,  AT=-A where AT is the transpose of matrix A. Then we…

Q: Given a square matrix 3 x 3 such that 2AA' = A' and Det(A) + 0, find Det(4). %3D

A: Let the square matrix of 3×3 is A s.t

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: If A is a square Matrix such that A'-A, what are the possible values of det A?

A: Determinant possible values

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: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

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Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

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Q: If A is a nonsingular matrix such that A2 = A, what is det(A)?

A: Given: A is a non-singular matrix such that A2=A. To find: A Solution: Non-singular matrix is a…

Q: If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the %3D value of trace of (A-!) ?…

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Q: With x and y as in your answer to question 3, the matrix

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Q: Which matrix is of the reduced echelon form? Oa. (1 2 04 0 0 2 7 Ob. 1 2 5 0 13-7 10 1 0 0 0 01 0…

A: To find the reduced echelon form of given matrices.

Q: Given the matrix 2 22 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

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Q: If A E Mpx, (C) nXn is a square matrix, and B is unitarily similar to А, then A and В have the same…

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Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

A:

Q: if A is (m*n) matrix, prove 'rank(AB) < max(rank(A), rank(B))' only A: (m*n), B : (n*k)

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Q: a) If A is a 5 x 5 skew symmetric matrix such that 5A + BT – 315 = 5(B – A)", 5 then |B| = ()".

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Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 1, a22 = 5, a33 = 4, a12 = 3, a13 = 2, and =…

A: Given A is 3×3 Symmetric matrix with entries a11=1 , a22=5 , a33=4 , a12=3a13=2 and a32=0.We know…

Q: Given the cofactor of matrix A, What is the adjoint of A?

A: Adjoint matrix is the transpose of cofactor matrix.

Q: Find a 3 x 3 matrix A such that Aa = 9x for all a in R³

A: We have to find matrix A such that Ax = 9x

Q: Use the reduce echelon form "triangle upper matrix" to find the det(A), where A = 2 -8 6 8 3 -9 5 10…

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Q: Prove that if A is an m x n matrix, B is an n x p matrix and C is a p x q matrix, then (AB)C= A(BC).

A:

Q: For given symmetric matrix A, find a diagonal matrix D that is congruent to A.

A: Given :      Symmetric matrix A   To find:           A diagonal matrix D that is congruent to A.

Q: Show that if A is any n × n matrix, then (a) A + AT is symmetric. (b) A − AT is skew symmetric.

A: Symmetric matrix: Any matrix A is symmetric matrix if and only if it is equal to its transpose that…

Q: Given the matrix 2 2 2 3 1 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: et A be the following matrix 2 7 2 4 4 8 2 3 3 fter diagonalization, Pand Dare found such that A =…

A:

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: Given that A is a 1 x 7 matrix and B is a 5 x 1 matrix. (a) Is AB defined? If so, what is the order…

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Q: If U is a square matrix such that UTU I, what can we say about det (U)?

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.