Exercise · ZW-MATRIX-008 · ★★☆ Intermediate
If \(\begin{pmatrix}a&2\\3&b+1\end{pmatrix}=\begin{pmatrix}4&2\\3&7\end{pmatrix}\), what are \(a\) and \(b\)?
Choose one option.
Show answer
- B. \(a=4,\; b=6\)
Explanation
Two matrices are equal when they have the same size and all their entries agree. Equating: \(a=4\) and \(b+1=7\), so \(b=6\).
Review the concept: Matrix
A matrix \(A\) is a rectangular array of numbers arranged in rows and columns; with \(m\) rows and \(n\) columns, it has size \(m\times n\).
\[A=\begin{pmatrix}a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ a_{m1}&\cdots&a_{mn}\end{pmatrix}\]
More practice problems: matrix
- ZW-MATRIX-001 What is the size of the matrix A=[1 2 3; 4 5 6]?
- ZW-MATRIX-002 In B=[7 0 -2; 5 9 1], what is the entry b_23 (row 2, column 3)?
- ZW-MATRIX-003 Compute A+B if A=[1 2; 3 4] and B=[0 1; -1 5].
- ZW-MATRIX-004 Compute 3A if A=[1 -2; 0 4].
- ZW-MATRIX-005 Which of the following matrices is square?
- ZW-MATRIX-006 What is the identity matrix of order 2?
- ZW-MATRIX-007 Compute A-2B if A=[3 1; 0 -2] and B=[1 0; 4 1].
- ZW-MATRIX-009 How many different 2× 2 matrices can be formed if every entry is 0 or 1?