Question

5. Construct a 3 x 4 matrix, whose elements are given by1) a

Answer 1

(i)

Given relation for the construction of 3×4 matrix is,

a ij = 1 2 | −3i+j |

The general 3×4 matrix is given as,

A=[ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ]

Here, the elements are given as,

a 11 = 1 2 | −3i+j | = 1 2 | −3×1+1 | = 2 2 =1

a 12 = 1 2 | −3i+j | = 1 2 | −3×1+2 | = 1 2

a 13 = 1 2 | −3i+j | = 1 2 | −3×1+3 | =0

a 14 = 1 2 | −3i+j | = 1 2 | −3×1+4 | = 1 2

a 21 = 1 2 | −3i+j | = 1 2 | −3×2+1 | = 5 2

a 22 = 1 2 | −3i+j | = 1 2 | −3×2+2 | = 4 2 =2

a 23 = 1 2 | −3i+j | = 1 2 | −3×2+3 | = 3 2

a 24 = 1 2 | −3i+j | = 1 2 | −3×2+4 | = 2 2 =1

a 31 = 1 2 | −3i+j | = 1 2 | −3×3+1 | = 8 2 =4

a 32 = 1 2 | −3i+j | = 1 2 | −3×3+2 | = 7 2

a 33 = 1 2 | −3i+j | = 1 2 | −3×3+3 | = 6 2 =3

a 34 = 1 2 | −3i+j | = 1 2 | −3×3+4 | = 5 2

Therefore,

A=[ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ] =[ 1 1 2 0 1 2 5 2 2 3 2 1 4 7 2 3 5 2 ]

Thus, the required matrix is A=[ 1 1 2 0 1 2 5 2 2 3 2 1 4 7 2 3 5 2 ] .

(ii)

Given relation for the construction of 3×4 matrix is,

a ij =2i−j

The general 3×4 matrix is given as,

A=[ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ]

Here, the elements are given as,

a 11 =2i−j =2×1−1 =1

a 12 =2i−j =2×1−2 =0

a 13 =2i−j =2×1−3 =−1

a 14 =2i−j =2×1−4 =−2

a 21 =2i−j =2×2−1 =3

a 22 =2i−j =2×2−2 =2

a 23 =2i−j =2×2−3 =1

a 24 =2i−j =2×2−4 =0

a 31 =2i−j =2×3−1 =5

a 32 =2i−j =2×3−2 =4

a 33 =2i−j =2×3−3 =3

a 34 =2i−j =2×3−4 =2

Therefore,

A=[ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ] =[ 1 0 −1 −2 3 2 1 0 5 2 3 2 ]

Thus, the required matrix is A=[ 1 0 −1 −2 3 2 1 0 5 2 3 2 ] .