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A) For the given matrix:

May 15, 2026Mathematics

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2 parts

2 \times 3

\begin{bmatrix} 5 & -3 \\ 0 & 7 \\ -4 & 3 \end{bmatrix}

x^2 - 2x + 1

5 steps

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Here's the solution:

For the given matrix

Identify the matrix.
The matrix shown is:
$A = \begin{bmatrix} 5 & 0 & -4 \\ -3 & 7 & 3 \end{bmatrix}$
Determine the order of the matrix.
The matrix has 2 rows and 3 columns.
The order of the matrix is $\boxed{2 \times 3}$ .
Find the transpose of the matrix.
The transpose of a matrix $A$ , denoted $A^T$ , is obtained by interchanging its rows and columns.
$A^T = \begin{bmatrix} 5 & -3 \\ 0 & 7 \\ -4 & 3 \end{bmatrix}$
The transpose of the matrix is $\boxed{\begin{bmatrix} 5 & -3 \\ 0 & 7 \\ -4 & 3 \end{bmatrix}}$ .

For the algebraic expression

Identify the expression.
The expression is $(x-1)^2$ .
Expand the expression.
Using the algebraic identity $(a-b)^2 = a^2 - 2ab + b^2$ , where $a=x$ and $b=1$ :
$(x-1)^2 = x^2 - 2(x)(1) + 1^2$ $= x^2 - 2x + 1$
The expanded form of $(x-1)^2$ is $\boxed{x^2 - 2x + 1}$ .

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