Matrices in Mathematics

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Questions and Answers

What is the total amount spent by the group in city X?

Rs 2500

Rs 4000

Rs 5000

Rs 3400 (correct)

What is the correct expression for calculating the total expenditure in paise for both cities?

A - B

A + B

A * B (correct)

B * A

What is the main purpose of arranging the information about Radha, Fauzia, and Simran?

To simplify their communication

To compare the prices of notebooks and pens

To express their possession of items in a clear format (correct)

To create a visual representation for marketing

How many pens does Fauzia possess according to the data?

2 Signup and view all the answers

How much was spent for Housecall in city Y?

Rs 2000 Signup and view all the answers

In which format is the possession of notebooks and pens expressed?

Matrix Signup and view all the answers

When performing the operation A + B, what will be the resulting matrix?

⎡ 3 7 ⎤ Signup and view all the answers

What does the first row of the second arrangement represent?

Number of notebooks held by each person Signup and view all the answers

What is the value of the expression 3A - C based on the matrices defined?

⎡ 7 -1 ⎤ Signup and view all the answers

What is a matrix defined as?

An ordered rectangular array of numbers or functions Signup and view all the answers

Which of the following correctly represents the number of notebooks held by Simran?

13 Signup and view all the answers

Which element of the matrix corresponds to Radha's possession of pens?

Row 1, Column 2 Signup and view all the answers

What type of data structure is NOT utilized in the context of the arrangement?

Scalar Signup and view all the answers

What is the matrix representation for point P(0, 1)?

⎡0 1⎤ Signup and view all the answers

In the matrix representation of quadrilateral ABCD, how many rows and columns does the matrix have?

2 rows and 4 columns Signup and view all the answers

What does the entry in the third row and second column of the workers' matrix represent?

Number of women workers in factory III Signup and view all the answers

What is the correct representation for the matrix based on the number of men and women workers in factories I, II, and III?

⎡30 25 25 31 27 26⎤ is not a valid matrix Signup and view all the answers

If a matrix has 8 elements, which of the following could be its possible order?

1 × 8 Signup and view all the answers

Which matrix correctly denotes the vertices of quadrilateral ABCD?

⎡1 3 1 -1⎤ Signup and view all the answers

What type of geometric figure can be represented using matrices based on the given information?

Only closed figures Signup and view all the answers

How many columns are found in the matrix representing the number of workers in factories I, II, and III?

2 columns Signup and view all the answers

What is required for the multiplication of two matrices A and B to be defined?

The number of columns of A must equal the number of rows of B. Signup and view all the answers

How is the (i, k)th element of the product matrix C calculated?

By multiplying the ith row of A and kth column of B element-wise and summing the results. Signup and view all the answers

If matrix A is of order 3 × 2 and matrix B is of order 2 × 4, what will be the order of the resulting product matrix C?

3 × 4 Signup and view all the answers

What is the sum expression used to derive the element cik of matrix C?

$ ext{cik} = ext{ai1} ext{b1k} + ext{ai2} ext{b2k} + ... + ext{ain} ext{bnk}$ Signup and view all the answers

Which of the following statements about matrix multiplication is true?

Matrix multiplication is associative. Signup and view all the answers

In the product matrix CD from the provided example, what was the order of the resulting matrix?

2 × 2 Signup and view all the answers

Which operation is performed when calculating the product of two matrices?

Element-wise multiplication followed by summing. Signup and view all the answers

If matrix A has dimensions 2 × 3 and matrix B has dimensions 3 × 2, what is true about their product AB?

It will result in a 2 × 2 matrix. Signup and view all the answers

What is the result of the matrix addition in the first equation when matrices are combined?

⎡a^2 + b^2 b^2 + c^2 ⎤ Signup and view all the answers

What operation is performed in the second part of the problem involving the matrices?

Matrix addition Signup and view all the answers

What is the correct output of multiplying the matrices ⎡a b⎤ and ⎡a -b⎤?

a^2 + b^2 Signup and view all the answers

Which of the following is the resulting matrix from the product of the specified matrices?

⎡1 -3 5⎤ Signup and view all the answers

What is the correct final output of multiplying the matrix ⎡2 -3⎤ by ⎡1 0⎤?

A single number 0 Signup and view all the answers

When multiplying the matrix ⎡3 -1 3⎤ by ⎡2⎤, what is the result produced?

7 Signup and view all the answers

For matrices where one is a column matrix and the other is a row matrix, what outcome do they usually produce when multiplied?

A square matrix Signup and view all the answers

In the provided problems, which of the following is an example of matrix transposition?

Reflecting the matrix across its leading diagonal Signup and view all the answers

Study Notes

Matrices as Representation of Information

Matrices can represent information in a structured way, like the possession of notebooks and pens by Radha, Fauzia, and Simran.
The arrangement of elements in the matrix reflects the information.
For example, in the matrix representing notebooks and pens, the first row represents Radha, Fauzia, and Simran's notebooks, while the second row represents their pens.

Formal Definition of a Matrix

A matrix is defined as an ordered rectangular array of numbers or functions.
These numbers or functions are called elements or entries of the matrix.
Matrices are denoted by capital letters.

Matrices as Representation of Geometrical Figures

Matrices can represent points and vertices of geometrical figures.
For Example, point P(0,1) can be represented by the matrix ⎡0 ⎤ ⎢ ⎥ ⎣1 ⎦
Matrices can represent a quadrilateral, with each row representing a vertex.

Multiplication of Matrices

The product of two matrices A and B is only defined if the number of columns of A equals the number of rows of B.
To find the (i, k)th element of the product matrix, you multiply the corresponding elements of the ith row of A and the kth column of B and sum the products.

Example of Matrix Multiplication

For example, if C = ⎡2 7⎤ and D = ⎡1 −1 2⎤, then the product CD is defined. ⎣0 3 4⎦ ⎢−1 1 ⎥
To find the elements of CD, you multiply the rows of C with the columns of D and sum the products.
Each entry of the product matrix represents the sum of products of corresponding entries in the row and column multiplied.

Matrix Multiplication Applications

Matrix multiplication can be used in real-world applications, like calculating the total amount spent by a group in different cities.
The matrix A represents the cost per contact of different types, and matrix B represents the number of contacts of each type in different cities.
Multiplying these matrices results in a matrix representing the total amount spent in each city.

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Description

This quiz covers matrices as a representation of information, including their formal definition and applications in geometry. Understand how matrices can structurally hold data and represent geometrical figures effectively.