Enter a 3 x 3 symmetric matrix A that has entries a1 = 1, a2 = 5, a33 = 4, a12 = 0, a31 = 3, and a A = 2 4

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: Find an SVD of the matrix. -6 5 A = 0 6

A: We have to general eigenvalue and eigenvectors to find Singular Value Decomposition of matrix A We…

Q: Explain why the matrix A + C does not exist.

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Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: Let A be an m×n matrix and let B be an n×p matrix. Show that if the columns of B are linearly​…

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Q: Demonstrate that A A-1 = A-1 A = I

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Q: Give an example of a 3 x 3 lower triangular matrix A that is not diagonal. A =

A: We write the 3x3 lower triangular matrix which is not diagonal

Q: B- Find the matrix A :- 3. A + -5 4 1. -1 3.

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Q: Find the echelon form of this augmented matrix, written so there are 1's on the diagonal. 1 -2 100…

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Q: Suppose that A is a 10 x 4 matrix, and that B is an equivalent matrix in echelon form. If the number…

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Q: Determine the cofactor of a13 in the matrix. 2 -4 A =5 4 4 -4

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Q: Calculate the rank of each matrix by converting it into canonical form…

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Q: If A is 5x4 matrix, and rank(A) = 1, then its nullity is 3.

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Q: Give an example of a nonzero 2 X 2 matrix A such that A2=O

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Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: Find a non-zero, two-by-two matrix such that: 6 -7 0 0 -30 35 0 0

A: Nonzero matrix and it's multiplication

Q: Find A of the matrix 1- A = 2. -4 2. 1.

A: The inverse of the matrix A of order n is defined as a matrix B of order n such that AB=BA=I, where…

Q: Find a 2 x 2 matrix such that -3 1

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Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

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Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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Q: Calculate the rank of each matrix by converting it into canonical form…

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Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

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Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

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Q: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

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Q: Find the matrix A (in terms of B, C, and D) if (4DA-'B )-1 = C

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Q: Enter a 3 x 3 symmetric matrix A that has entries au = 5, az2 = 4, a33 = 0, a12 = 2, a3ı = 1, and…

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Q: Enter a 3×3 symmetric matrix A that has entries:  a11=0 a22=2 a33=5 a12=4 a13=3 a23=1

A: Symmetric Matrix : If A be an n×n square matrix , then A is symmetric if aij = aji ; where 1≤i,j≤n .

Q: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: Use the method of Example 6 to compute the matrix A10, where 1 0 A = -3 2

A: The given matrix is A=10-32. Observe that, A2=10-32 10-32=10-94=10-3·22-122A3=10-94…

Q: If A is an invertible square matrix that is row equivalent to matrix B , then both A and B are row…

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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: Determine if the columns of the given matrix form a linearly dependent set. 3 4 3 1 3 -2 0 -1 -7 5.…

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Q: Determine whether the matrix is symmetric.

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Q: Show that if A is a square matrix that satisfies the equation A2 - 2A + I = O, then A-1 = 2I - A.

A: Given that,                    A2-2A+I=0

Q: B: find A of the matrix 2 1 3 3 2 -1 -4 3 -1

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Q: Put as many 1's as possible in a 4 by 7 echelon matrix U whose pivot columns are(a) 2, 4, 5…

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Q: Enter a 3 x 3 skew-symmetric matrix A that has entries a12 = 1, a13 = 3, and a32 = 4.

A: Skew Symmetric Matrix: If the transpose of a matrix A is equal to the negative of itself then the…

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: If the __________ of a matrix is p× q, then p represents the number of __________ and q represents…

A: If the order of a matrix is p x q, then p represents the number of rows and q represents the number…

Q: Give an example of a 4 by 4 matrix A, which is not symmetric, however A is symmetric.

A: A square matrix is said to be symmetric if it is symmetric about the main diagonal.

Q: Use the following matrix. A = -1 −2 0 3 2 1 5 2 1 What is the sum of matrix A and its…

A: Given, A=-1-20321521

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5x5)) =

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Q: 2. Let the rref of a matrix A be, 1 0 2 0 -2) 0 1 -5 0 -3 0 0 1 6 Determine A if the first, second…

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Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

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Q: ) If A is a square matrix such that some row of A² is a linear combination of the other rows of A²,…

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