Multiply the given matrix. After performing the multiplication, describe what happens to the elements in the first matrix. begin{bmatrix}a_{11} & a_{12} a_{21} & a_{22} end{bmatrix}begin{bmatrix}1 & 0 0 & 1 end{bmatrix}

Falak Kinney

Falak Kinney

Answered question

2021-01-28

Multiply the given matrix. After performing the multiplication, describe what happens to the elements in the first matrix. [a11a12a21a22][1001]

Answer & Explanation

gwibdaithq

gwibdaithq

Skilled2021-01-29Added 84 answers

Step 1
Given: [a11a12a21a22][1001]
Step 2
Let matrix A=[a11a12a21a22] & matrix B=[1001]
we have to find the multiplication of matrices A&B that means we have to find A×B
We know the formula for multiplication of 2×2 matrices.
[a11a12a21a22][b11b12b21b22]=[a11b11+a12b21a11b12+a12b22a21b11+a22b21a22b12+a22b22]
Step 3
Here from matrix A we get,
a11=a11,a12=a12,a21=a21,a22=a22
from matrix B we get,
b11=1,b12=0,b21=0,b22=1
Thus matrix multiplication A×B becomes,
[a11a12a21a22][1001]=[(a11×1)+(a12×0)(a11×0)+(a12×1)(a21×1)+(a22×0)(a22×0)+(a22×1)]
=[a11+00+a12a21+00+a22]
=[a11a12a21a22]
Step 4
Therefore we get,
A×B=[a11a12a21a22]
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

Jeffrey Jordon

Expert2022-01-24Added 2605 answers

Answer is given below (on video)

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