Linear Algebra Examples

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Linear Algebra
Find the Result of 5 Times the 5x5 Identity Matrix 5
5
Step 1
The identity matrix or unit matrix of size 5 is the 5×5 square matrix with ones on the main diagonal and zeros elsewhere.
[1000001000001000001000001]
Step 2
Multiply the scalar 5 by the identity matrix.
5[1000001000001000001000001]
Step 3
Simplify.
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Step 3.1
Multiply 5 by each element of the matrix.
[5⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2
Simplify each element in the matrix.
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Step 3.2.1
Multiply 5 by 1.
[55⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.2
Multiply 5 by 0.
[505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.3
Multiply 5 by 0.
[5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.4
Multiply 5 by 0.
[50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.5
Multiply 5 by 0.
[500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.6
Multiply 5 by 0.
[5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.7
Multiply 5 by 1.
[50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.8
Multiply 5 by 0.
[500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.9
Multiply 5 by 0.
[5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.10
Multiply 5 by 0.
[50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.11
Multiply 5 by 0.
[500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.12
Multiply 5 by 0.
[5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.13
Multiply 5 by 1.
[50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.14
Multiply 5 by 0.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.15
Multiply 5 by 0.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.16
Multiply 5 by 0.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.17
Multiply 5 by 0.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.18
Multiply 5 by 0.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.19
Multiply 5 by 1.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]
Step 3.2.20
Multiply 5 by 0.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]
Step 3.2.21
Multiply 5 by 0.
[5000005000005000005005⋅05⋅05⋅05⋅1]
Step 3.2.22
Multiply 5 by 0.
[50000050000050000050005⋅05⋅05⋅1]
Step 3.2.23
Multiply 5 by 0.
[500000500000500000500005⋅05⋅1]
Step 3.2.24
Multiply 5 by 0.
[5000005000005000005000005⋅1]
Step 3.2.25
Multiply 5 by 1.
[5000005000005000005000005]
[5000005000005000005000005]
[5000005000005000005000005]
 [x2  12  π  ∫⁡xdx ]