Name: Solving the Systems Using Cramer's Rule
Uploaded: 2019-07-19
Duration: 15 min 2 s
Description: In this video, you will learn how to solve the system of linear equations with the help of cramer's rule? So let's watch this video to know more about this concept.

Question

Find the adjoint of the following matrix:

[\begin{array}{lll} 2 1 2 \\ 2 2 1 \\ 1 2 2 \end{array}]

Accepted Answer

The given matrix is $A = {(a_{i j})}_{3 \times 3}$

$A_{ij} and M_{ij}$ respectively are cofactor and minor of $a_{i j}$ .

$A_{11} = (- 1)^{1 + 1} |\begin{array}{ll} 2 1 \\ 2 2 \end{array}| = 2$

$A_{12} = (- 1)^{1 + 2} |\begin{array}{ll} 2 1 \\ 1 2 \end{array}| = - 3$

$A_{13} = (- 1)^{1 + 3} |\begin{array}{ll} 2 2 \\ 1 2 \end{array}| = 2$

$A_{21} = (- 1)^{2 + 1} |\begin{array}{ll} 1 2 \\ 2 2 \end{array}| = 2$

$A_{22} = (- 1)^{2 + 2} |\begin{array}{ll} 2 2 \\ 1 2 \end{array}| = 2$

$A_{23} = (- 1)^{2 + 3} |\begin{array}{ll} 2 1 \\ 1 2 \end{array}| = - 3$

$A_{31} = (- 1)^{3 + 1} |\begin{array}{ll} 1 2 \\ 2 1 \end{array}| = - 3$

$A_{32} = (- 1)^{3 + 2} |\begin{array}{ll} 2 2 \\ 2 1 \end{array}| = 2$

$A_{33} = (- 1)^{3 + 3} |\begin{array}{ll} 2 1 \\ 2 2 \end{array}| = 2$

$∴ A d j A = [\begin{array}{lll} A_{11} A_{21} A_{31} \\ A_{12} A_{22} A_{32} \\ A_{13} A_{23} A_{33} \end{array}] = [\begin{matrix} 2 & 2 & - 3 \\ - 3 & 2 & 2 \\ 2 & - 3 & 2 \end{matrix}]$

Find the adjoint of the following matrix: $[\begin{array}{lll} 2 1 2 \\ 2 2 1 \\ 1 2 2 \end{array}]$

Important Questions on Determinants

Learn and Prepare for any exam you want !

Find the adjoint of the following matrix: 2 1 22 2 11 2 2

Important Questions on Determinants

Learn and Prepare for any exam you want !

Find the adjoint of the following matrix: $[\begin{array}{lll} 2 1 2 \\ 2 2 1 \\ 1 2 2 \end{array}]$