In order for a linear system with augmented matrix [A | b] to be consistent, what mustbe true about the ranks of A and [A | b]?

Q: 1 3 -4 2 0 0 0 0 0 0 0 0 -1 6. 1 -3 7 1 4 -3 0 0

A: Remark:  We know that the maximum number of linearly independent vectors in a matrix is equal to the…

Q: Let A be the augmented matrix of a linear system. Find the solution for this linear system

A: Given,

Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

A:

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

A:

Q: If A is a 4 X 2 matrix, explain why the rows of A must be linearly dependent.

A: If A is a 4 x 2 matrix, then it has 4 rows and 2 columns. Each row can be thought of as a vector in…

Q: 1 -3 5 Let A = -3 -4 1 2 6 1 -1 -8 1 with augmented matrix [A]b] is always consistent. How many…

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Q: write the augmented matrix associatedwith the given system.

A:

Q: Let Ax = b be a linear system with real coefficients such that A is an m × n matrix and Ax = b has a…

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Q: Write the linear system corresponding to the reduced augmented matrix. [100 47 0116 0 0 00 O No…

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Q: 7 |-4 [3 а 4

A: Augmented matrix173a-44170a-21-416apper triangular formx+7y=-40.x+y(a-21)=16Equivalent system

Q: Let A be a 5 x 4 matrix and b a nonzero vector in R5. We are told the system Ar = b has infinitely…

A: Given A be a 5 x 4 matrix and b a nonzero vector in R5 That is, there are 4 equations and  unknown…

Q: If A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent.

A: In A is a 3 X 5 matrix, explain why the columns of A must be linearly dependent. You have 5 column…

Q: Write the linear system whose augmented matrix is [ 1 3 4 0 (a) 3 -1 2 3 -2 1 -4 3 1 3 4 | 0 3 -1 2…

A: Part (a) Given augment matrix is 2         1        3    4  ⋮  03      -1        2    0  ⋮   3-2…

Q: The linear system Ax=b is consistent whenever the columns of [A | b] are linearly dependent. True

A: Introduction: If and only if b is a linear combination of A's column vectors, a linear system Ax = b…

Q: 1 1 5 -3 1 2 -2|-1 7 15 k -4 For what value of k will the system have no solutions? k =

A: Consider the system of equations: a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3 This system of…

Q: 10. Techbabble.com makes plasma relays, chroniton scanners, and pulse sequencers. Each relay…

A: To determine the number of plasma relays, chroniton scanners, and pulse sequencers should they…

Q: Exercise 1214 Find h such chai 3h 12 is uhe augmenied mari of a consinen sysem

A: The given system is, It is given that the system is consistent.

Q: 1 -5 5g 011 -6h 3 4-9k

A:

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.