Show that the matrix A given below is singular. A = -2

Q: Find the elementary matrix E such that EB = A where 2 -12 2 1 1 A = 4 0. -2 and B = 24 %3D | 6. -8 3…

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Q: Find the elementary matrix E such that EB = A where %3D 2 3 1 2 3 1 A = 4 -3 -2 and B = -8 6 4 7 -6…

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Q: Find a matrix B such that AB = I, where 4 1 1 0 A = and I = -4 4 1 a b Hint: Let B c d B =

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

A: Given:

Q: .

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Q: Find values of a for which the following matrix is not invertible: 1 a+ a 2

A: 1a+1a-24

Q: In Exercise, find the singular values of the given matrix.

A: Given matrix will be as:- A = 1100   and   AT= 1010 Now,  ATA = 11001010 = 1+1000=2000 To Find the…

Q: Which of the following about matrix A is not true? A = [1 2 2 3 [3 1 31 3] 1 2]

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Q: Find x such that the matrix is singular. X 3 A = -7 2 X =

A: Singular Matrix - A matrix is said to be singular if and only if its determinant is equal to zero.

Q: ) Find a matrix A such that 3 A -3 1 1 EEE A =

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Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

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Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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Q: Determine whether the given matrix A is diagonalizable. If so, find a matrix P that diagonalizes A…

A: Given matrix A=01-12 and A=200121-101To find: A matrix P that diagonalizes A and a diagonal matrix…

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: Let [ 2 A = 6 -1 and B = %3D Find an elementary matrix E such that EA=B.

A: An elementary matrix is one which differs from the identity matrix by one elementary row operation.

Q: Identify a nonzero 2x2 matrix that is invertible but not diagonalizable. Choose the correct answer…

A: Diagonalization

Q: Determine whether A is similar B .If A ∽B, give an invertible matrix P such that P-1 AP = B.

A:

Q: In Exercise, find the singular values of the given matrix.

A: Find the product for the matrix A and transpose of A.…

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

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Q: Let A and B be -1 0 10-3 A = 10-3 -1 0 2 1 2 1 2 2 Find an elementary matrix E such that EB = A.

A: Given that: A=-10210-3122B=10-3-102122

Q: The matrix A = is an orthogonal matrix. True O False

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Q: (a) Given the matrix A= , use Cayley-Hamilton Theorem to show that: [e1 e4: 21 ను

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Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

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: Find a 3 × 2 matrix T, such that TT' = A, where 4 A = |4 3 3 5

A: Given: To find a 3 x 2 matrix T, such that TT' = A,  A = 540453035

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: Find a 3 x 3 matrix A such that A A A A = 0 0 = 2 5 0 3 and

A: Given A100=-1-41,  A010=251  and A001=003

Q: In Exercise, find the singular values of the given matrix.

A: Consider a matrix A. Now, let λ1,λ2,λ3... be the eigen values of the matrix AAT. Now, the singular…

Q: In Exercise, find the singular values of the given matrix.

A: We have the given matrix A as A=34 Now, transpose of matrix A is calculated as AT=34 Now, the value…

Q: Let A be a 2 x 2 matrix. If det (A) # 0, then det (adj A) = det (A).

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Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: a) Let A be a 3 x 5 matrix

A: For the multiplication of two matrix the number of columns in first matrix is equal to the number of…

Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

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Q: If A is an orthogonal matrix, then det(A) = ±1.

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Q: In Exercise, find the singular values of the given matrix.

A: Consider  A=2102. Now ATA=20122102=2223

Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 1 5 1 A = 0 2 1 0 0 2

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Q: If A is a square matrix such that A3 = O, show that (I-A)~l = I + A + A2.

A: To prove that (I-A)~l = I + A + A2 If A is a square matrix such that A3 = O

Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0

Q: (BH) Recall that a matrix Q is orthogonal if Q' Q = I.

A: Given, A matrix Q is orthogonal if QTQ=I Proof: (a) The one way to write the norm for vector x is…

Q: Let A be a nonsingular 4 x 4 matrix such that |A-1| = -2, then AT.adj(A-}) Select one: O True O…

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Q: Find the value of k such that matrix A is singular: (1 2 A = | 5 -1 2 6. k.

A: Singular Matrix: A square matrix that is not invertible is called singular or degenerate i.e., it is…

Q: Let A = 3 0 -1 2 Compute the indicated matrix. (If this is not possible, enter DNE in any single…

A: Solve  for the A^3

Q: Find the value of k such that matrix A is 2. k – 10 singular on Ik - 5 а. 1 С. 3 b. 2 d. 4 O D O B O…

A: Topic = matrices Correct option=D

Q: a For what values of a, b, and c is the matrix -a invertible?

A: For no values of a, b, c the given matrix is invertible.

Q: Determine whether A is similar B .If A ∽B, give an invertible matrix P such that P-1 AP = B.

A: The given matrices are A=110011001 and  B=110010001. Here, it is observed that the matrices A and B…

Q: Find the matrix A such that 1 0 A = -1 -2 9. 7 11 a b Hint: Let A = c d A =

A: If two matrix are equal then all elements of matrices are equal. In this question first we find…

Q: Find x such that the matrix is singular. x 5 A = -3 2

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Q: O Prove that if a matrix A satisfies A² = A, then I — 2A = (I — 2A)−¹.

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

A: Given det(A) = 6