Name: Finding Inverse by Elementary Transformations
Uploaded: 2019-07-19
Duration: 12 min 5 s
Description: In this video, we will learn to find the inverse of matrices using elementary transformations of matrices. We will learn how to find the inverse of a matrix,...

Question

There are two families

A

and

B

. In family

A

there are

4

men,

6

women and

2

children and in family

B

there are

2

men,

2

women and

4

children. The recommended daily amount of calories is

2400

for men,

1900

for women,

1800

for children and

45

gram of protein for men,

55

grams for women and

33

grams for children. Represent the above information using matrices. By matrix multiplication, calculate the total requirement of calories and proteins for each of the two families.

Accepted Answer

Given there are two families $A$ , and $B$ such that

Number of Men Number of Women Number of Children

$A$ $4$ $1900$ $2$

$B$ $2$ $2$ $4$

Let us represent the recommended daily amount of calories, and proteins in the tabular form:

Men Women Children

Calories $2400$ $1900$ $1800$

Proteins $45$ $55$ $33$

Now, to calculate the total requirement of calories, and proteins by each of the two families.

Let the matrix representing the families be given by

$P = [\begin{matrix} 4 & 6 & 2 \\ 2 & 2 & 4 \end{matrix}]$

And, the matrix representing the calories, and proteins requirement be given by

$Q = [\begin{matrix} 2400 & 45 \\ 1900 & 55 \\ 1800 & 33 \end{matrix}]$

Thus, the total requirement of calories, and proteins by each of the two families is given by

$P Q = [\begin{array}{l} 4 & 6 & 2 \\ 2 & 2 & 4 \end{array}] [\begin{array}{l} 2400 & 45 \\ 1900 & 55 \\ 1800 & 33 \end{array}]$

$= [\begin{matrix} (2400 \times 4) + (1900 \times 6) + (1800 \times 2) & (4 \times 45) + (6 \times 55) + (2 \times 33) \\ (2 \times 2400) + (2 \times 1900) + (4 \times 1800) & (2 \times 45) + (2 \times 55) + (4 \times 33) \end{matrix}]$

$= [\begin{matrix} 9600 + 11400 + 3600 & 180 + 330 + 66 \\ 4800 + 3800 + 7200 & 90 + 110 + 132 \end{matrix}]$

$= [\begin{matrix} 24600 & 576 \\ 15800 & 332 \end{matrix}]$

Hence, Calories requirement for families $A$ and $B$ are $24600$ and $15800$ respectively.

And, Proteins requirement for families $A$ and $B$ are $576$ and $332$ respectively.

Important Questions on Matrices

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