Answered: Determine whether the span of the…

Determine whether the span of the column vectors of the given matrix A is equal to R^3. Show your work and justify your answer. 1 1 1 A=1 2 0 1 0 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

See similar textbooks

Related questions

Q: What is the relationship between a matrix and the i-hat and j-hat vectors

A: matrix is used to find the cross product of two vectors detailed solution is given below

Q: lues of a 4 x 4 matrix A are given by 2, 1,5, 4, the

A: We have to choose the correct answer from the given option according to the given condition

Q: Determine all values of the parameters x and y such that the vector 1 s in the range of the above…

Q: Find a 3 by 3 matrix that scales the point (x,y,z) by 2 in the x direction and 4.5 in the direction,…

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

Q: Suppose that a 3×3 matrix A has three columns C1, C2, C3 which span the plane given by x + 2y – 5z =…

Q: The i th row vector of a matrix product AB can be computed by multiplying A by the ith row vector of…

A: Given statement is The i th row vector of a matrix product AB can be computed by multiplying A by…

Q: 7. Find a 2 x 2 matrix that reflects vectors in the (x, y) plane across the x axis. 8. Find a 2× 2…

Q: The nullspace of a 5 by 5 matrix contains only x = 0 when the matrix has ___ pivots. The column…

Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: For vectors of length N and matrices of size N x N, what order of magnitude of flops does it take to…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: sorry but I indicate in the question above that its needs to be transformed into a lower triangular…

A: Given matrix is A = 1-13-1402-2110010-20100011-10 Note:- This is not a square matrix so, we can…

Q: Find the coordinate matrix of x = (1, 2, −1) in R3 relative to the (nonstandard) basisB′ = {u1, u2,…

Q: Explain column vector of m x 1 matrix?

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: Define the term matrix equation.

Q: High order of tensor cannot be represented by matrix

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2. Write the matrix that could be used to rotate a vector 200 degrees clockwise about the origin.…

A: We have to find the matrix that could be used to rotate a vector 200 degrees clockwise about the…

Q: Determine if the column space of the matrix A included contains the vector(11,−9,5,7). If so,…

A: Given below the detailed solution.

Q: Write down the 2 by 2 matrix that a) project every vector onto x¡ axis. b) rotate a vector clockwise…

A: We have to solve given problem:

Q: Express the product Ax as a linear combination of the column vectors of A. 2 3][3 -4 + 2 3 5 + 3 |…

A: To find out the correct option.

Q: find the inuerse matrix of motrix 1 2.Use +he Laploce expan si on of the column. 4 0 1 6 0 3

Q: Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given, B=1331

Q: Explain why the row vectors of a 7 x 2 matrix form a linearly dependent set. (Assume all matrix…

A: Rank of the matrix is at most min(7,2) = 2 dimension of row space = rank of matrix

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: Apply Gram- Schmidt process to the vectors 3

Q: What is the multiplicative identity property? (applied to matrices and scalars)

A: Given: multiplicative identity property

Q: Find the equilibrium vector of the matrix P : algebraically. Be sure to properly normalize the…

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 X and Y be symmetric matrices both size 15x15. Decide if Z = XT(X+Y) is a symmetric matrix too.…

A: Given, X & Y are symmetric matrices. So, XT = X and, YT = Y Given, Z = XT(X+Y) So, ZT =…

Q: Proivde Definitions of Vectors and Matrices?

A: Vector: A vector is a group of numbers whether it is in row or in column. vector is also a matrix.…

Q: Compute the matrix product by expressing it in the form of linear combination of column vectors and…

Q: High order of tensor cannot be represented by matrix ulgn İhi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: stable

Q: Suppose an organism moves down a sloped surface along the steepest line of descent, i.e., the…

Q: What must be a if the vectors (1,-a,1,1). (-1,a+2,–2, a –1), (0,2, –1,a² +a-4) are linearly…

A: We have to solve given problem:

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: Show the process of Reflecting a vector/matrix about a line that goes through the origin?

A: Reflection of vector/matrix about a line that goes through the origin: When we reflex a point about…

Q: Can you provide a summary of potential applications for Hermitian Matrices? Please cite any…

Q: Describe when the multiplication of two matrices is not defined.

A: Given, multiplication of two matrices

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: Find the basis of column space of the matrix A given in the attached image .Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1,…

Q: State the dimension of the matrix.

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

Q: Express the product Ax as a linear combination of the column vectors of A. 1 21 3 + 3 +3 2.

A: The given product, A2×2x2×1=12-3432 Which will result into a vector of order 2×1

Q: Find the stable vector of this Matrix: 0 0 1 0 1/2 1/2 1/3 2/3 0

A: A stable vector is a probability vector such that PW=W.Let W=xyz. Then, we have 0010121213230xyz=xyz…

Concept explainers

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.

Question

Determine whether the span of the column vectors of the given matrix A is equal to
R^3. Show your work and justify your answer.
1 1 1
A = 1 2 0
1 0 1
|

Expert Solution

Step 1: We determine whether element's of R^3 is in span of column vectors of A Or not as follow

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.
Determine if the statement is true or false. If the statement is false, then correct it and make it true. A 75 matrix has 5 rows.
Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.