(a) The set of all 2 × 2 symmetric matrices is a subspace of R²×². Find a basis for this subspace, and find the coordinates of -1 in that basis.

Q: Find a basis for the space of 2 × 2 lower triangular matrices. Basis =

A:

Q: Find a base for the line space of the matrix and determine the line rank.

A:

Q: Find the rank of the matrices where x, y, and z are distinct.

A: We have to find the rank of the matrix

Q: Find the change-of-coordinates matrix from Bto the standard basis in Rn.

A:

Q: Find ∣A−1∣ for the matrix

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Q: What is the basic way to find a basis for all of the vectors x y z  that satisfies the matrix…

A: Given a 3×3 matrix. A=R1R2R3 where R1, R2 and R3 are the three rows with three columns, i.e. three…

Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: In Exercises 19-20, find the inverse of each of the following 4×4 matrices, where k₁, k₁, k3, k₁,…

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Q: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: luate the number. P(7,4)

A:

Q: Find a basis for the space of 2 by 3 matrices whose nullspace contains (2, 1, 1 ).

A: To Find : The basis for the space of  2×3 matrices whose nullspace contains (2, 1, 1 ).

Q: Find a basis for the row space of the matrix 1 1 02 2 2 2 2 -1 -1 -2 0 A

A:

Q: Create a 2 × 2 matrix with the components -1, 1, and 0 such that when you multiply the matrix with a…

A: The reflection across x-axis means the matrix transforms one vector (x,y) to the vector (x,-y).

Q: Find a formula for the dimension of the vector space of symmetric n X n matrices.

A: Given: symmetric  n×nmatrix

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.