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Chapter 3: 15P (page 88)

Find the rank of each of the following matrices.

(112246325)

Short Answer

Expert verified

The rank of the matrix112246325is 2 .

Step by step solution

01

Given information

The given matrix is112246325

02

Definition of the rank of a matrix

The number of non-zero rows remaining in a row reduced matrix is called the rank of a matrix.

03

Apply row operations to reduce the matrix into row reduction form

Consider the matrix A =112246325

Multiply row 1 by and subtract the result from row 2.

A=112022325 R2-2R1

Multiply row 1 by -3and subtract the result from row 3.

A=1120220-1-1 role="math" localid="1653389234639" R3-3R1

Divide the second row by 2.

A=1120110-1-112R2

Add row 2 to row 3.

A=112011000R3卤R2

The row reduced form of the given matrix is 112011000

Here, the total number of non-zero rows is 2. Hence, the rank of the matrix

A=112246325is2

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Most popular questions from this chapter

Let each of the following matrices M describe a deformation of the(x,y)plane for each given Mfind: the Eigen values and eigenvectors of the transformation, the matrix Cwhich Diagonalizesand specifies the rotation to new axesrole="math" localid="1658833126295" (x',y')along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.

role="math" localid="1658833142584" (3113)

Find the Eigen values and Eigen vectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.

(3-2-20)

Question: For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using

6.{x+y-z=13x+2y-2z=3

Let each of the following represent an active transformation of the vectors in ( x ,y )plane (axes fixed, vector rotated or reflected as in Example 3, show that each matrix is orthogonal, find its determinant and find its rotation angle, or find the line of reflectionthe

C=[0-1-10]

Verify the details as indicated in diagonalizing H in (11.29).
See all solutions

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