Suppose matrix product ab is defined. (a) if a is 4 x 7 and b is a column matrix, give the dimensions of b and ab. [4 marks] (b) if a is the identity matrix and b is 5 x 5, what size is a? [4 marks] (c) if a is 4 x 5 and ab is 4 x 7, what size is b?

(a) Order of matrix B is 7 × 1 and order of matrix AB is 4 × 1.

(b) Order of matrix A is 5 × 5.

(c) The order of matrix B is 5 × 7.

Step-by-step explanation:

The product of two matrices is possible if and only if column of first matrix is equal to row of second matrix.

If A is an n × m matrix and B is an m × o matrix, their matrix product AB is an n × p matrix,

(a)

It is given that order of matrix A is 4 x 7.

B is a column matrix. It means the number of column in matrix B is 1.

Let the order of matrix B = n × 1

Product of matrices A and B is possible if and only if column of matrix A is equal to row of matrix B.

Order of matrix B is 7 × 1

Order of matrix AB is 4 × 1.

(b)

Order of matrix B = 5 × 5

It is given that A is the identity matrix.

Identity matrix is a square matrix having 1s on the main diagonal, and 0s everywhere else.

So, order of matrix A is equal to order of matrix B.

Order of matrix A = 5 × 5

Therefore order of matrix A is 5 × 5.

(c)

Order of matrix A = 4 × 5

Order of matrix AB = 4 × 7

Let Order of matrix B = n × m

Product of A and B are possible if and only if n=5.

On comparing both sides, we get

Therefore the order of matrix B is 5 × 7.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.