Write the result obtained by— (a) adding 1 to every term in the generalised form. (b) doubling every term in the generalised form

Question

Homi · Accepted Answer

We will perform two operations on a given set of algebraic expressions.

Step 1 — Identifying the Generalised Form

Let us first write down the given generalised form. It is a set of numbers using a variable 'm'.

\begin{pmatrix} m + 3 & m - 4 & m + 1 \\ m - 2 & m & m + 2 \\ m - 1 & m + 4 & m - 3 \end{pmatrix}

Step 2 — Adding 1 to Every Term

We need to add the number 1 to each term. This means we add 1 to every expression.

For the first term in Row 1: $(m + 3) + 1$ $= m + 4$

For the second term in Row 1: $(m - 4) + 1$ $= m - 3$

For the third term in Row 1: $(m + 1) + 1$ $= m + 2$

For the first term in Row 2: $(m - 2) + 1$ $= m - 1$

For the second term in Row 2: $(m) + 1$ $= m + 1$

For the third term in Row 2: $(m + 2) + 1$ $= m + 3$

For the first term in Row 3: $(m - 1) + 1$ $= m$

For the second term in Row 3: $(m + 4) + 1$ $= m + 5$

For the third term in Row 3: $(m - 3) + 1$ $= m - 2$

So, the new generalised form after adding 1 to each term is:

\begin{pmatrix} m + 4 & m - 3 & m + 2 \ m - 1 & m + 1 & m + 3 \ m & m + 5 & m - 2 \end{pmatrix} }$$

Step 3 — Doubling Every Term

Now, we need to double each term. This means we multiply every expression by 2.

For the first term in Row 1: $2 \times (m + 3)$ $= 2m + 6$

For the second term in Row 1: $2 \times (m - 4)$ $= 2m - 8$

For the third term in Row 1: $2 \times (m + 1)$ $= 2m + 2$

For the first term in Row 2: $2 \times (m - 2)$ $= 2m - 4$

For the second term in Row 2: $2 \times (m)$ $= 2m$

For the third term in Row 2: $2 \times (m + 2)$ $= 2m + 4$

For the first term in Row 3: $2 \times (m - 1)$ $= 2m - 2$

For the second term in Row 3: $2 \times (m + 4)$ $= 2m + 8$

For the third term in Row 3: $2 \times (m - 3)$ $= 2m - 6$

So, the new generalised form after doubling each term is:

\begin{pmatrix} 2m + 6 & 2m - 8 & 2m + 2 \ 2m - 4 & 2m & 2m + 4 \ 2m - 2 & 2m + 8 & 2m - 6 \end{pmatrix} }$$

Answer

(a) Adding 1 to every term: Row 1: m + 4, m - 3, m + 2 Row 2: m - 1, m + 1, m + 3 Row 3: m, m + 5, m - 2 (b) Doubling every term: Row 1: 2m + 6, 2m - 8, 2m + 2 Row 2: 2m - 4, 2m, 2m + 4 Row 3: 2m - 2, 2m + 8, 2m - 6

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