Name: The Applications of Matrices
Uploaded: 2019-07-19
Duration: 7 min 47 s
Description: Let's learn the applications of matrices, such as solving homogenous and non-homogenous linear equations, the Gauss-Jordan method, and the reduction method.

Question

A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}], C_{3} + 2 C_{2}

and then

3 R_{3}

. What will you conclude if we first do

3 R_{3}

and then

C_{3} + 2 C_{2}

.

Accepted Answer

The given matrix is $A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}]$ .

$A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}]$

If the elements of $i^{th}$ row or column are multiplied by a non-zero number $k$ , then it is denoted as $R_{i} \to {kR}_{j}$ or $C_{i} \to {kC}_{j}$ .

Apply the given transformation $C_{3} + 2 C_{2}$ , first multiplying the second column with $2$ and then adding the third column of matrix $A$ .

Let $P$ be the new matrix after transformation so,

$\Rightarrow P = [\begin{matrix} 1 & - 1 & 3 + (- 2) \\ 2 & 1 & 0 + (2) \\ 3 & 3 & 1 + (6) \end{matrix}]$

$\Rightarrow P = [\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & 2 \\ 3 & 3 & 7 \end{matrix}]$ .

Now apply the given transformation $R_{3} \to 3 R_{3}$ by multiplying the third row of the matrix $P$ with $3$ .

Let $Q$ be the new matrix after transformation so,

$Q = [\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & 2 \\ 3 \times 3 & 3 \times 3 & 7 \times 3 \end{matrix}]$

$= [\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & 2 \\ 9 & 9 & 21 \end{matrix}]$

Therefore, the required matrix is $[\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & 2 \\ 9 & 9 & 21 \end{matrix}]$ .

If we first do $3 R_{3}$ and then $C_{3} + 2 C_{2}$ then the final matrix will be same and we can conclude that the transformations are commutative.

$A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}], C_{3} + 2 C_{2}$ and then $3 R_{3}$ . What will you conclude if we first do $3 R_{3}$ and then $C_{3} + 2 C_{2}$ .

Important Questions on Matrices

Learn and Prepare for any exam you want !

A=1-13210331,C3+2C2 and then 3R3. What will you conclude if we first do 3R3 and then C3+2C2.

Important Questions on Matrices

Learn and Prepare for any exam you want !

$A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}], C_{3} + 2 C_{2}$ and then $3 R_{3}$ . What will you conclude if we first do $3 R_{3}$ and then $C_{3} + 2 C_{2}$ .