Find Upper B squaredB2​, if possible.
Upper BB
equals=
left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 5 2nd Column 2 2nd Row 1st Column 4 2nd Column 1 EndMatrix right bracket −5	2	4	1

You provided a matrix \( B \) and are asking for \( B^2 \) (the matrix squared). To calculate \( B^2 \), we multiply matrix \( B \) by itself.

The matrix \( B \) is:

\[
B = \begin{pmatrix}
-5 & 2 \\
4 & 1
\end{pmatrix}
\]

To compute \( B^2 \), we need to perform the matrix multiplication \( B \times B \):

\[
B^2 = \begin{pmatrix}
-5 & 2 \\
4 & 1
\end{pmatrix}
\times
\begin{pmatrix}
-5 & 2 \\
4 & 1
\end{pmatrix}
\]

Now let's compute the product:

1. The element in the first row, first column is:
\[
(-5 \times -5) + (2 \times 4) = 25 + 8 = 33
\]

2. The element in the first row, second column is:
\[
(-5 \times 2) + (2 \times 1) = -10 + 2 = -8
\]

3. The element in the second row, first column is:
\[
(4 \times -5) + (1 \times 4) = -20 + 4 = -16
\]

4. The element in the second row, second column is:
\[
(4 \times 2) + (1 \times 1) = 8 + 1 = 9
\]

Thus, \( B^2 \) is:

\[
B^2 = \begin{pmatrix}
33 & -8 \\
-16 & 9
\end{pmatrix}
\]

So the matrix \( B^2 \) is:

\[
\boxed{\begin{pmatrix}
33 & -8 \\
-16 & 9
\end{pmatrix}}
\]

Would you like more details or have any questions? 

Here are 5 related questions for practice:
1. How do you compute the product of two \( 2 \times 2 \) matrices in general?
2. What is the determinant of matrix \( B \)?
3. How can you find the inverse of matrix \( B \), if it exists?
4. What is the trace of matrix \( B^2 \) (the sum of its diagonal elements)?
5. How do eigenvalues relate to matrix powers like \( B^2 \)?

**Tip:** To square a matrix, remember that matrix multiplication is not commutative: \( A \times B \neq B \times A \) in general.

Find B^2, if possible. B = [ [ -5, 2 ], [ 4, 1 ] ]

Learn how to calculate the square of a 2x2 matrix B with a detailed step-by-step solution. This problem covers key concepts in matrix algebra, including matrix multiplication techniques. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation