Let A=( -2 0 1 3 -1 2 7 -5 6 -6 -3 4 ) (a) W

Let A=( -2 0 1 3 -1 2 7 -5...

Key Concepts

Matrix Entry Notation

Matrix entry notation typically specifies the position of an element in a matrix using two indices, usually in the form (i, j), where i refers to the row number and j refers to the column number. This concept is essential for accurately identifying and manipulating individual elements within a matrix.

Row and Column Extraction

Row and column extraction involves selecting all elements from a single row or a single column of a matrix. This process is useful for analyzing data, applying transformations, or decomposing matrices into simpler, more manageable components for further computation in linear algebra.

Matrix Dimensions

Matrix dimensions describe the size of a matrix in terms of the number of rows and columns it contains. Knowing the dimensions is fundamental because it determines the structure of the matrix and is critical for performing any matrix operations, such as addition, multiplication, or solving systems of linear equations.

Transcript

00:01 In the given question, the following matrix a is given to have the elements 1113 -2046 -1137.

00:19 And now we are asked about this matrix like we are asked five questions regarding the matrix a.

00:29 So the first question is the size of the matrix a.

00:35 The size of the matrix a.

00:37 So how do we write the size of a matrix? so we can write it over here.

00:44 The size of a matrix, size of a matrix is written as the number of rows, the number of rows by the number of codens that is present in the matrix so this is how we would write the size of any matrix so over here we can count the number of rows of the matrix a first right so we will see that it has one two and three rows right so three rows by next let's count the number of columns in the matrix a it has one two three and four columns so three by four is the size of the matrix a now let's move on to the next part of the question we are asked what is the third column of a the third column of a so start to count the columns from the left side of the matrix.

02:00 So this means we can count the columns as this is the first column, this is the second column, and this is the third column, and this is the fourth column.

02:14 So the third column of the matrix a can be written as one, four, three, right? so this would be the third column.

02:25 Of the matrix a.

02:27 Now let's move on to the third question that is asked, which is what is the second row of the matrix a? the second row of the matrix a.

02:43 So again, when we are counting the rows, we start to count from the top of the matrix.

02:49 So this is the first row.

02:54 This would be the second row and this would be the third row of the matrix a so when we write the second row it has the elements two zero four and six right so we can write the answer as two zero four six so this would be the second row of a moving on to the fourth part which is asked to us we are told what we are asked what is the element of a in three -tooth position so we have to find the element in three -two three -tooth position so what does this mean so three -two means this the first number over here denotes the first number first number denotes the row number first number denotes the row number and the second number let's write it in green right we have written all the rows in green so let's write it like this first number in the bracket is giving us the row number of the matrix and the second number of the matrix and the second number number the second number is giving us the column number so this means the element to be found the element to be found is in is in is in is in the third row is in the third row and the second column the second column so we can go back to the matrix that is given to us and we can see that the third row is having the elements 1137 right and now let's see which is the second column right so this is the second column so this is the second column...

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