Falak Kinney

2021-01-28

Multiply the given matrix. After performing the multiplication, describe what happens to the elements in the first matrix.
$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

gwibdaithq

Skilled2021-01-29Added 84 answers

Step 1

Given:$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Step 2

Let matrix$A=\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]$
& matrix $B=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

we have to find the multiplication of matrices A&B that means we have to find$A\times B$

We know the formula for multiplication of$2\times 2$ matrices.

$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{cc}{b}_{11}& {b}_{12}\\ {b}_{21}& {b}_{22}\end{array}\right]=\left[\begin{array}{cc}{a}_{11}{b}_{11}+{a}_{12}{b}_{21}& {a}_{11}{b}_{12}+{a}_{12}{b}_{22}\\ {a}_{21}{b}_{11}+{a}_{22}{b}_{21}& {a}_{22}{b}_{12}+{a}_{22}{b}_{22}\end{array}\right]$

Step 3

Here from matrix A we get,

${a}_{11}={a}_{11},{a}_{12}={a}_{12},{a}_{21}={a}_{21},{a}_{22}={a}_{22}$

from matrix B we get,

${b}_{11}=1,{b}_{12}=0,{b}_{21}=0,{b}_{22}=1$

Thus matrix multiplication$A\times B$ becomes,

$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}({a}_{11}\times 1)+({a}_{12}\times 0)& ({a}_{11}\times 0)+({a}_{12}\times 1)\\ ({a}_{21}\times 1)+({a}_{22}\times 0)& ({a}_{22}\times 0)+({a}_{22}\times 1)\end{array}\right]$

$=\left[\begin{array}{cc}{a}_{11}+0& 0+{a}_{12}\\ {a}_{21}+0& 0+{a}_{22}\end{array}\right]$

$=\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]$

Step 4

Therefore we get,

$A\times B=\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]$

Thus after multiplication of matrices A & B we get again the matrix which equals A.

After multiplication of two matrices the elements in the first matrix remains same.

Given:

Step 2

Let matrix

we have to find the multiplication of matrices A&B that means we have to find

We know the formula for multiplication of

Step 3

Here from matrix A we get,

from matrix B we get,

Thus matrix multiplication

Step 4

Therefore we get,

Thus after multiplication of matrices A & B we get again the matrix which equals A.

After multiplication of two matrices the elements in the first matrix remains same.

Jeffrey Jordon

Expert2022-01-24Added 2605 answers

Answer is given below (on video)

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