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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Write out the matrix that matches the given description.

A = [ a i j ] 3 × 2 w i t h a i j = 2 i j .

A = [ a i j ] 4 × 2 w i t h a i j = ( 1 ) i j .

B = [ b i j ] 2 × 4 w i t h b i j = ( 1 ) i + j .

B = [ b i j ] 3 × 4 w i t h b i j = 1 i f i < j a n d b i j = 0 i f i j .

C = [ c i j ] 4 × 3 w i t h c i j = i + j i f i j a n d c i j = 0 i f i < j .

C = [ c i j ] 4 × 3 w i t h c i j = 0 i f i j a n d c i j = 1 i f i = j

(a)

To determine

The matrix that matches the given condition, A=[aij]3×2 with aij=2ij.

Explanation

Given information:

A=[aij]3×2 with aij=2ij.

Explanation:

The dimension of matrix A is 3×2.

Now, aij=2ij.

For i=1,j=1a11=2(1)1=1

For i=1,j=2a12=2(1)2=0

For i=2,

(b)

To determine

The matrix that matches the given condition, A=[aij]4×2 with aij=(1)ij.

(c)

To determine

The matrix that matches the given condition, B=[bij]2×4 with bij=(1)i+j.

(d)

To determine

The matrix that matches the given condition, B=[bij]3×4 with bij=1 if i<j and bij=0 if ij.

(e)

To determine

The matrix that matches the given condition, C=[cij]4×3 with cij=i+j if ij and cij=0 if i<j.

(f)

To determine

The matrix that matches the given condition, C=[cij]4×3 with cij=0 if ij and cij=1 if i=j.

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