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In this Class 12 Mathematics topic from the Matrix chapter, students learn when two matrices are considered equal. They examine the requirement that both matrices have the same order and that every pair of corresponding elements is equal. The topic also shows how matrix equality can be used to compare entries, form equations, and find unknown values. Clear examples help students apply these conditions accurately in algebraic problems.
TOPIC PRACTICE
Quiz this set
Up to 3 questions from this page. Select your focus, then start.
If \(A=\begin{bmatrix}x&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}5&2\\3&4\end{bmatrix}\) and \(A=B\), what is the value of \(x\)?
Correct answer: D
For two equal matrices, their corresponding entries are equal. Here the (1,1) entries are \(x\) and \(5\), so \(x=5\). Option C (4) might mislead since 4 appears in the (2,2) position, but equality demands comparing the same positions, not different ones. Exam tip: always equate entries at the same row and column indices when matrices are equal (compare (i,j) with (i,j)).
If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), which statement is correct?
Correct answer: B
Two matrices are equal only if they have the same order and every corresponding entry is equal. Both A and B are 2×2 and entries (1,2,3) match, but the (2,2) entries are 4 and 5 which are different. Hence A ≠ B. Option A is wrong because one corresponding entry differs; option C is wrong because both matrices have the same order (2×2); option D is wrong because neither matrix is a zero matrix. Exam tip: to test equality check order first, then compare each corresponding element one by one.
If \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) and \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) and \(A=B\), what is \((x,y)\)?
Correct answer: A
Equal matrices have equal corresponding entries. From the (1,1) entry we get \(x=3\), and from the (2,2) entry \(y=4\). Hence \((x,y)=(3,4)\). The closest distractor \((4,3)\) is wrong because it swaps the values of x and y. Exam tip: always equate entries at the same (row,column) positions when comparing matrices.
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