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Chapter 3: 17P (page 88)


Short Answer

Expert verified

The rank of the matrix1143311074214102064is2.

Step by step solution

01

 Step-by-Step Solution Step 1: Given information

The given matrix is.

02

 Step 2: 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.

Multiply row 1 by 3 and divide row 3 by

Subtract row 1 from row 2 and row 4 from row 3.

Divide row 1 by 3, row 4 by 2 and multiply row 3 by 2.

Subtract row 1 from row 4 and add row 2 to row 3.

Divide row 2 by.

Add row 4 to row 2.

The row reduced form of the given matrix is.

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

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Most popular questions from this chapter

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

(-121230103)

Find the symmetric equations (5.6)or(5.7)and the parametric equations (5.8) of a line, and/or the equation (5.10) of the plane satisfying the following given conditions.

Line through(4,-1,3) and parallel to i-2k.

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.

9.{x-y+2z=52x+3y-z=42x-2y+4z=6

Find the eigenvalues and eigenvectors of the real symmetric matrix

M=(AHHB)

Show that the eigenvalues are real and the eigenvectors are perpendicular.

Question: Verify that each of the following matrices is Hermitian. Find its eigenvalues and eigenvectors, write a unitary matrix U which diagonalizes H by a similarity transformation, and show thatU-1+HU is the diagonal matrix of eigenvalues.(-23+4i3-4i-2)
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