Construct a 3×4 matrix, whose elements are given by (i) aij=21∣−3i+j∣ (ii) aij=2i−j

Question

Construct a 3×4 matrix, whose elements are given by (i) aij​=21​∣−3i+j∣ (ii) aij​=2i−j

Filo · Accepted Answer

In general  a 3×4 matrix is given by,A=⎣⎡​a11​a21​a31​​a12​a22​a32​​a13​a23​a33​​a14​a24​a34​​⎦⎤​ (i) aij​=21​∣−3i+j∣,i=1,2,3andj=1,2,3,4∴a11​=21​∣−3×1+1∣=21​∣−3+1∣=21​∣−2∣=22​=1a21​=21​∣−3×2+1∣=21​∣−6+1∣=21​∣−5∣=25​ a31​=21​∣−3×3+1∣=21​∣−9+1∣=21​∣−8∣=28​=4a12​=21​∣−3×1+2∣=21​∣−3+2∣=21​∣−1∣=21​ a22​=21​∣−3×2+2∣=21​∣−6+2∣=21​∣−4∣=24​=2a32​=21​∣−3×3+2∣=21​∣−9+2∣=27​a23​=21​∣−3×2+3∣=21​∣−6+3∣=21​∣−3∣=23​ a33​=21​∣−3×3+3∣=21​∣−9+3∣=21​∣−6∣=26​=3a14​=21​∣−3×1+4∣=21​∣−3+4∣=21​∣1∣=21​ a24​=21​∣−3×2+4∣=21​∣−6+4∣=21​∣−2∣=22​=1a34​=21​∣−3×3+4∣=21​∣−9+4∣=21​∣−5∣=25​ Therefore, the required matrix is A=⎣⎡​125​ 4​21​ 223​ ​023​ 3​21​ 125​ ​⎦⎤​ (ii) aij​=2i−j,i=1,2,3andj=1,2,3,4∴a11​=2×1−1=2−1=1a21​=2×2−1=4−1=3a31​=2×3−1=6−1=5a12​=2×1−2=2−2=0a22​=2×2−2=4−2=2a32​=2×3−2=6−2=4a13​=2×1−3=2−3=−1a23​=2×2−3=4−3=1a33​=2×3−3=6−3=3a14​=2×1−4=2−4=−2a24​=2×2−4=4−4=0a34​=2×3−4=6−4=2Therefore, the required matrix is A=⎣⎡​135​024​−113​−202​⎦⎤​

Question Text	Construct a $3 \times 4$ matrix, whose elements are given by (i) $a_{ij} = \frac{1}{2} ∣ - 3 i + j ∣$ (ii) $a_{ij} = 2 i - j$
Answer Type	Text solution:1
Upvotes	150

Construct a $3 \times 4$ matrix, whose elements are given by
(i) $a_{ij} = \frac{1}{2} ∣ - 3 i + j ∣$
(ii) $a_{ij} = 2 i - j$

Text solutionVerified

Practice questions from similar books

Construct a 3×4 matrix, whose elements are given by (i) aij​=21​∣−3i+j∣ (ii) aij​=2i−j

Text solutionVerified

Practice questions from similar books

Construct a $3 \times 4$ matrix, whose elements are given by
(i) $a_{ij} = \frac{1}{2} ∣ - 3 i + j ∣$
(ii) $a_{ij} = 2 i - j$