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Questions  >>  CBSE XII  >>  Math  >>  Matrices
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Q)

Construct a 3 x 4 matrix,whose elements are given by: $\;a_{ij}=2i-j$

Note: This is a 2 part question, split as 2 separate questions here.

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A)
Toolbox:
  • In general given a matrix $A_{3\times 4}$ its elements are given by $A=\begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14}\\a_{21} & a_{22} & a_{23} & a_{24}\\a_{31} & a_{32} & a_{33} & a_{34}\end{bmatrix}$ where (i, j) = (1,2,3,4).
Given that $a_{ij}=2i-j \Rightarrow$
  • $a_{11}=2\times 1-1=1.$
  • $a_{12}=2\times 1-2=0.$
  • $a_{13}=2\times 1-3=-1.$
  • $a_{14}=2\times 1-4=-2.$
 
  • $a_{21}=2\times 2-1=3.$
  • $a_{22}=2\times 2-2=2.$
  • $a_{23}=2\times 2-3=1.$
  • $a_{24}=2\times 2-4=0.$
  •  
  • $a_{31}=2\times 3-1=5.$
  • $a_{32}=2\times 3-2=4.$
  • $a_{33}=2\times 3-3=3.$
  • $a_{34}=2\times 1-4=2.$
Hence the required matrix is $A=\begin{bmatrix}1 & 0 & -1 & -2\\3 & 2 & 1 & 0\\5 & 4 & 3 & 2\end{bmatrix}$

 

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