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Multiplication of Matrices

If ℝ is the s...

Question

If $R$ is the set of all real numbers, what do the cartesian products $R \times R$ and $R \times R \times R$ represent?

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Solution

The cartesian product $R \times R$ represents the set $R \times R = {(x, y) : x, y \in R}$ which represents the co-ordinates of all the points in two - dimensional space and the cartesian product $R \times R \times R$ represents the set $R \times R \times R = {(x, y, z) : x, y, z \in R}$ which represents the co-ordinates of all points in three - dimensional space.

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Similar questions

K = {k : 0 \leq k \leq 1, k \in R},

R

is the set of all real numbers is

R

be the set of Real numbers. Define the real function

f : R \to R

f (x) = x + 10

and sketch the graph of this function.

A = {(x, y) \in R \times R | 2 x^{2} + 2 y^{2} - 2 x - 2 y = 1},

B = {(x, y) \in R \times R | 4 x^{2} + 4 y^{2} - 16 y + 7 = 0}

C = {(x, y) \in R \times R | x^{2} + y^{2} - 4 x - 2 y + 5 \leq r^{2}}

.
Then the minimum value of

| r |

A \cup B \subseteq C

Q. Write the following as intervals:

(i) {x : x \in R, - 4 < x \leq 6}

(i i) {x : x \in R, - 12 < x < - 10}

(i i i) {x : x \in R, 0 \leq x < 7}

(i v) {x : x \in R, 3 \leq x \leq 4}

: R \to R

g : R \to R

be two non-constant differentiable functions. If

f^{'} (x) = (e^{(f (x) - g (x))}) g^{'} (x)

x ϵ R

f (1) = g (2) = 1

, then which of the following statement(s) is (are) TRUE?

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Multiplication of Matrices

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