Question

Try It! Understand Identity Matrices

a b
3. a. What is the product of
a
?
c d]

Answer 1

Answer:The product of the matrix [a b; c d] and the identity matrix [1 0; 0 1] is the original matrix itself, [a b; c d]. thank you.

Answer 2

`\sf \left[\begin{array}{cc}a & b \\ c & d\end{array}\right]`

Explanation:

The product of the matrices

`\sf \left[\begin{array}{cc}a & b \\ c & d\end{array}\right]`

and

`\sf \left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]`

is found by multiplying the corresponding elements in each row of the first matrix with the corresponding elements in each column of the second matrix and summing the products.

The resulting matrix will have the same dimensions as the original matrices.

Let's perform the matrix multiplication:

`\sf \left[\begin{array}{cc}a & b \\ c & d\end{array}\right] * \left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] \\\\ = \left[\begin{array}{cc} (a * 1 + b * 0) & (a * 0 + b * 1) \\(c * 1 + d * 0) & (c * 0 + d * 1)\end{array}\right] \\\\ = \left[\begin{array}{cc} a & b \\ c & d \end{array}\right]`

So, the product of the given matrices is the original matrix:

`\sf \left[\begin{array}{cc}a & b \\ c & d\end{array}\right]`