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CBSE Class 12 RD Sharma Maths Determinants Exercise 6.1
Exercise 6.1

(2) Evaluate the following determinants:(iii) $\left| \begin{matrix} \cos {{15}^{\circ }} & \sin {{15}^{\circ }} \\ \sin {{75}^{\circ }} & \cos {{75}^{\circ }} \\ \end{matrix} \right|$ (iv) $\left| \begin{matrix} a+ib & c+id \\ -c+id & a-ib \\ \end{matrix} \right|$

, , , , ,

(iii) As per the question it is given that, $\left| \begin{matrix} \cos {{15}^{\circ }} & \sin {{15}^{\circ }}  \\ \sin {{75}^{\circ }} & \cos {{75}^{\circ }}  \\ \end{matrix} \right|$...

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1. Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (vii) $A=\left[ \begin{matrix} 2 & -1 & 0 & 1 \\ -3 & 0 & 1 & -2 \\ 1 & 1 & -1 & 1 \\ 2 & -1 & 5 & 0 \\ \end{matrix} \right]$

, , , , ,

(vii) Assume ${{M}_{ij}}$  and ${{C}_{ij}}$ represents the minor and co–factor of an element, where i and j represent the row and column. The minor of matrix can be obtained for particular element...

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1. Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (v) $A=\left[ \begin{matrix} 0 & 2 & 6 \\ 1 & 5 & 0 \\ 3 & 7 & 1 \\ \end{matrix} \right]$ (vi) $A=\left[ \begin{matrix} a & h & g \\ h & b & f \\ f & f & c \\ \end{matrix} \right]$

, , , , ,

(v) Assume ${{M}_{ij}}$ and ${{C}_{ij}}$ represents the minor and co–factor of an element, where i and j represent the row and column. The minor of matrix can be obtained for particular element by...

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1. Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (iii) $A=\left[ \begin{matrix} 1 & -3 & 2 \\ 4 & -1 & 2 \\ 3 & 5 & 2 \\ \end{matrix} \right]$ (iv) $A=\left[ \begin{matrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \\ \end{matrix} \right]$

, , , , ,

(iii) Assume ${{M}_{ij}}$ and ${{C}_{ij}}$ represents the minor and co–factor of an element, where i and j represent the row and column. The minor of the matrix can be obtained for a particular...

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1. Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (i) $A=\left[ \begin{matrix} 5 & 20 \\ 0 & -1 \\ \end{matrix} \right]$ (ii) $A=\left[ \begin{matrix} -1 & 4 \\ 2 & 3 \\ \end{matrix} \right]$

, , , , ,

(i) Assume ${{M}_{ij}}$ and ${{C}_{ij}}$ represents the minor and co–factor of an element, where i and j represent the row and column. The minor of the matrix can be obtained for a particular...

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