-[:: ]~•[:] a b a B Consider the matrices A and B c d Show how you use the dot product definition to calculate ONLY the entry in row two and column one of the matrix BA.

Q: Find the inverse of the matrix using elementary matrices.

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Q: Using only the definition of matrix multiplication, prove that multiplication of matrices is…

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Q: Find two different 2x2 matrices A and B such that AB = BA. %3D --. .. (Use a comma to separate…

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Q: Determine the dimension of the matrix. 0 7 15 0   −3 0 3 3 −1 1 6 7

A: Explanation of the solution is given below....

Q: Find inverse of matrix 1  2  3 0  4  5 0  0  6 Using augmented matrix  Show work

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Q: Find an orthogonal basis for the column space of the matrix to the right. -1 2 -8 4 1 -2 7 1 - 4 - 3

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Q: matrices

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Q: Why is it important that the matrix is invertible? Give and example.

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Q: Give an example of two matrices A and B such that BA exists, but AB is undefined. Explain why your…

A: Finding the product of two matrices is only possible when the inner dimensions are the same, meaning…

Q: For Fxerrice determine the inverse of the given matrix if possible. Otherwise, state that the matrix…

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Q: Find the size of the matrix. Determine if it is 9 6 3 1 39 6 1 9

A: Count the number of rows and columns

Q: (c) Using matrices, find the images of the points (1,7), (-4,5) and (8,2) under a translation of +6…

A: Write the matrix as x and y coordinate. Then proceed  xy = 1-48752

Q: A diagonal matrix is a square matrix that if rotated to give the original matrix 1- right 2-Error

A: a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term…

Q: The product of two invertible matrices is always non-zero. Select one: OTrue

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Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: (a) Find the matrix A so that AB=C, where а, а, а, B= b, b, b, & C= b, b, b, a, az az (2 rows are…

A: Given B=a1a2a3b1b2b3c1c2c3 now using row operation R1↔R3 ~c1c2c3b1b2b3a1a2a3

Q: Use (ii) of the rank of a matrix by row reduction theorem to find the rank of the given matrix. (?…

A: The given matrix is 7-113.

Q: the matrix A = and explain why or why not this matrix is diagonalizable

A: In the given question, concept of diagonalizable matrix is applied. Diagonalizable Matrix Any square…

Q: Make yourself familiar with the alternative notations. What is the simplest way to describe the…

A: We have to find out the simplest way to describe the product of A and v. The matrix A is given, that…

Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

Q: The vector -201 3 is a linear combination of the vectors 10 5 -3 and -9 if and only if the matrix…

A: Answer is in next step.

Q: Find two 3 x 3 matrices A and B such that A · B+ B · A Find a 3 x 3 matrix A that is not the zero…

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Q: Determine if the columns of the matrix span `R^{4}`. Give your arguments.

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Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Construct a 4x4 matrix to rotate 60° about the z-axis and rotate 30° about the x-axis and then…

A: Here we need to find out the 4x4 matrix to rotate 60 degrees to z axis and 30 degrees to x axis also…

Q: Let y = and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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Q: L- matrix and U

A: The objective of the question is determine the L- and U- matrix.

Q: For each part of this question you Justiy your ansuer with reason/Explanaticns. a) gf A is any 4x4…

A: The objective is to explain the statements a) If A is any 4×4 matrix then columns of A span ℝ4 b)…

Q: a b Find all 2x2 matrices that commute with A=| ос)

A: if B matrix commute with A then AB = BA

Q: Use matrix multiplication to find the compression of (-2, 2) in the x-direction with factor k = 1/2.…

A: We have to use matrix multiplication to find the compression of (-2, 2) in the x-direction with…

Q: Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such…

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Q: Let A and B be n × n matrices and let x ∈ Rn. How many scalar additions and multiplications are…

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Q: Consider the matrix

A: Given, the matrix                    A=1-101-1121-141-10-112-2042-282-2

Q: Diagonalize the matrix if possible [ 0 1 1 2 1 2 3 3 2 ].

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Q: 4. and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

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Q: Find the trace of the matrix A =

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Q: Perform Block Multiplications of Matrices A and B; i.e., find AB where: 1 0 1 2 3 4 0 1 5 6 7 8. A =…

A: The multiplication of 2 matrices is possible only when the number of colmuns of the first matrix is…

Q: Consider the matrices A = and B c d Show how you use the dot product definition to calculate ONLY…

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Q: Prove that if A and B are square matrices and AB is invertible, then both A and B are invertible.…

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Q: Which of the matrices are orthogonal (has orthonormal columns)? V3 1 1 1 1 -2 v2 V3 2 -2 1 1 1 3. 2…

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Q: Find LU factorization of the matrix A =

A: In this question, we apply Gauss's elimination method to find the A=LU form. A is given by…

Q: Find values for the variables so that the matrices are equal. image 1 =image 2

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Q: V3 Express 1 as a product of elementary matrices.

A: Solve by matrices

Q: (0 8 1 1 4 -1

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Q: Let y = and u= 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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Q: Matrix A is 2 x 7 and matrix B is 2 x 8. BTA is dimension

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Q: A and B are two sequar upper triangular matrix then ove that the JAB| is equal the product of its…

A: Topic:- matrix algebra

Q: Let y= Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u. and u=…

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Q: Let y= and u= Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u.…

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