How do i do matrics? if....?

Question

A={-1,0}
{0, 5}

B= {3 0 2}

C={1 6 0}
{-5 0 -3}
{0 4 -1}

D={8}
{9}

1) Name an element in matrix A
2)Name a coulumn matrix
3) Name a row matrix
4) Name the square matrices
5) give the dimensions of matrix B
6) The number 4 in matrix c is in what position?
7) Multiply matrix A times D is the answer [-8 -45}?


please tell me how you get these answers because i have never done matrics and i do not have a book. thank you to anyone who helps

Answer 1

1) An element is just any one of the four numbers there. 0 or 5 or -1 would be an acceptable answer here.

2) D is a column matrix. A column matrix has only one column (although it can have several rows, like D has 2 rows).

3) B. It only has one row. Just like #2.

4) A and C. The dimensions of a matrix are (number of rows) by (number of columns), written m×n. Any matrix with the same number of rows as columns is "square" - why the call it that should be apparent.

5) B has one row and three columns, so it's 1×3. Remember, this isn't a "times" - it's like in a 2×4 piece of wood, it's indicating the dimensions of the matrix.

6) A position is written (row, column). 4 is in the third row, second column, so it's in the position (3,2).

7) It cannot be. When matrices multiply it must be like this:

(m by n matrix) (n by k matrix) = (m by k matrix)

Notice they MUST share that inside dimension, and must result in a new matrix with the outside dimensions.

If A times D were [-8 45], it would mean:
(2×2) (2 × 1) = (1×2)

The inside dimensions work, but the result [-8 45] has the wrong dimensions, it ought to be 2×1, not 1×2.

For more, see:
http://en.wikipedia.org/wiki/Matrix_%28mathematics%29
http://en.wikipedia.org/wiki/Matrix_multiplication

Answer 2

1) A={-1,0}
{0, 5}
any one of -1, 0,0,5 is an element

2) D={8}
{9} is a column matrix with one column only

3) B= {3 0 2} is a row matrix with one row.

4)A={-1,0}
{0, 5}
is a square matrix with 2 rows and 2 columns

5) B is a 1 x 3 matrix (1 row, 3 column)

6) C={1 6 0}
{-5 0 -3}
{0 4 -1}
4 is the 3-2 element on row 3 column 2

70 A x D
Multiply matrix A times D is the answer [-8 -45}?
{-1,0}
{0, 5}
x
(8)
(9)
=
{-8}
{45}
so ti's not [-8 -45]

Answer 3

1) an element is any number or letter in that matrix.
2) D
3)B
4)C and A
5)1X3
6)Row 3, column 2
7) A is a 2X2 matrix, and D is a 1X2. You cannot multiply them. Think of the orders: 2X2 and 1X2. The Inner numbers must be the same (where I have "2 and 1". The outer numbers are both 2. You can multiply D*A because that gives 1X2 and 2X2. The inner numbers are the same. The result will be a 1X 2 ( the outer numbers, 1 and 2).

Answer 4

Matrices are rectangular groups of numbers. If you have this matrix:
{ a b c}
{ d e f }
{ g h i }

Then { d e f } is an example of a row matrix. It's just one row of the larger matrix. Likewise,
{ c }
{ f }
{ i }
is an example of a column matrix. It's just one column of the larger matrix.

The large matrix is 3-by-3. The row matrix is a 3-by-1 matrix. The column matrix is a 1-by-3 matrix. You list the vertical size, followed by the horizontal size, when describing matrix dimensions.