Chapter 1.3

Question 0

A matrix with only one column

Answer 0

A column vector or a column matrix.

Question 1

Def: A matrix

Answer 1

A rectangular array of numbers, the numbers in the array are called entries in the matrix.

Question 2

A matrix with only one row

Answer 2

A row vector or a row matrix

Question 3

The size of a matrix

Answer 3

The m number of rows and n number of columns denoted as mxn

Question 4

Numerical quantities when discussing matrices

Answer 4

Scalars

Question 5

A matrix with n rows and n columns

Answer 5

A square matrix of order n

Question 6

Th entries a11, a22, … , ann of a square matrix A

Answer 6

The main diagonal of A

Question 7

Def: two equal matrices

Answer 7

Two matrices with the same size and whos corresponding entries are equal

Question 8

Def: the sum of two matrices of the same size

Answer 8

The matrix obtained by adding the entries of B to the corresponding entries of A. Matrices of different sized cannot be addes.

Question 9

Def: the difference of two matrices of the same size

Answer 9

The matrix obtained by subtracting the entries of B from the corresponding entries of A. Matrices of different sized cannot be subtracted.

Question 10

Def: A scalar multiple of A

Answer 10

The product cA where c is any scalar, cA is a matrix obtained by multiplying each entry of A by c.

Question 11

Matrix multiplication

Answer 11

If A is an mxr matrix and B is an rxn matrix the product AB is the mxn matrix whos entries are determined as follows:
To find the entry in row i and column j of AB, single out row i from A and column j from B. Multiply the corresponding entries from the row and column together. The sum of the resulting products is the entry ABij.

Question 12

What is required by the definition of matrix multiplication?

Answer 12

That the number of columns in the first factor equals the number of rows in the second factor.

Question 13

If A1, A2, … , Ar are matrices of the same size and c1, c2, … , cr are scalars, then the expression of the form c1A1 + c2A2 + … + crAr is called…

Answer 13

A linear combination of A1, A2, … , Ar with coefficients c1, c2, … , cr

Question 14

If A is an mxn matrix, and if x is an nx1 column vector, then the product Ax can be expressed as

Answer 14

A linear combination of the column vectors of A in which the coefficients are the entries of x

Question 15

The transpose of an mxn matrix A

Answer 15

The definition is the nxm matix that results from interchanging the rows and columns of A, that is: the first row of A is the first column of the transpose of A

Question 16

The trace of A (denoted tr(A))

Answer 16

If A is a square matrix, the trace is the sum of the entries along the main diagonal.

Question 17

A smaller matrix achieved by inserting horisontal and vertical rules between selected rows and columns (and the name of the method)

Answer 17

Submatrix achieved through partitioning

Question 18

The row or column method to compute rows or columns of AB

Answer 18

j:th column vector of AB = A[j:th column vector of B]

I:th row vector of AB = [i:th row vector of A]B