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What is the concept of matrix rank in linear algebra
First of all, you can regard a matrix as row vectors or column vectors, and then the so-called rank is the rank of these row vectors or column vectors, that is, the number of vectors contained in the maximally independent group. It can be proved that row rank is equal to column rank in a matrix, that is, row rank and column rank are equivalent in quantity, that is, the rank of a matrix
Rank of linear algebraic matrix
Finding the rank of a matrix
A=2 1 8 3 7
2 -3 0 7 -5
3 -2 5 8 0
1 0 3 2 0
A = 2 18 3 72 - 3 07 - 53 - 2 58 01 0 3 2 01, 4 rows exchange - 1 03 20 21 8 3 72 - 3 07 - 53 - 2 58 0 cancel the first column - 1 03 200 12 - 1 70 - 3 - 6 4 - 50 - 2 - 4 20 cancel the second column - 1 03 200 12 - 1 700 01
1. The divisor does not change. When the divisor is divided by 5, the quotient is 12.5. The original quotient is ()
2. When a number is expanded 10 times, it is 9.9 times larger than the original number
3. A and B also walk 12 kilometers. A walks 5 kilometers per hour, half the way, and then 3 kilometers per hour. B always walks 4 kilometers per hour. So ()
1. B first to the end 2, a first to the end 3, at the same time
Note:
1、2.5
If the divisor is reduced five times, the quotient is increased five times
So 12.5 / 5 = 2.5
2、1.1
Let X be the original number
Then 10x-x = 9.9
X＝1.1
3. (2) B comes first
It took 3.2 hours for a to complete the journey and three hours for B
In the parallelogram ABCD, e is a point on CD, de: CE = 2:3, connecting AE, be and BD, and AE and BD intersect at point F, then s △ def: s △ EBF: s △ ABF
First of all, the area formula is S & nbsp; = & nbsp; 1 / 2 (bottom * height). Since it is the area ratio, you can ignore 1 / 2. Secondly, find common points in these three triangles and try to simplify the formula: the first two triangles share the same edge ef, and use it as the bottom, so their area ratio is reduced to the ratio of high; the last two triangles share the same point B, Since both of them are related to the second triangle, we can regard it as the base point s △ def: s △ EBF & nbsp; = & nbsp; Da: BB (assuming that a and B are the vertical points of two triangles respectively), DA / / BB, the triangles are similar, Da: BB = DF: BF, DF: BF = de: ab = 2:5, s △ def: s △ EBF & nbsp; =2: 5 & nbsp; & nbsp;, s △ def = 2 / 5 & nbsp; & nbsp; s △ EBF & nbsp; s △ EBF: s △ ABF & nbsp; = & nbsp; EF: AF = de: ab = 2:5 (triangle similarity) & nbsp;, s △ ABF & nbsp; = 5 & nbsp; / 2 & nbsp; s △ EBF s △ def: s △ EBF & nbsp;: s △ ABF & nbsp; = & nbsp; 2 / 5:1:5 / 2 = 4:10:25
Simple calculation of 2.25x4.8 + 89.5x0.48-12x0.48
2.25x4.8+89.5x0.48-12x0.48=（2.25+8.95-1.2)x4.8=48
Square root
When a large number, how to quickly square out, such as the root sign 1681, how to quickly out plus or minus 41, please advise - thank you
First estimate that the sum of squares 1600 is close to (or equal to) 40,
According to the law of the square of the last position: 1 and 9 are 1,
Then square 41 or 49
In the parallelogram ABCD, AC intersects BD at point O, AE is perpendicular to BD and point E, the angle ead is equal to 60 degrees, AE is equal to 2cm, AC plus BD is equal to 14cm
⊙ AE ⊥ BD in e
∴∠AED=90°
∵∠EAD=60°
∴∠ADE=30°
∴AD=2AE=4cm
ABCD is a parallelogram
∴BC=AD=4cm
∵AC+BD=14cm
∴OB+OC=7cm
∴△BOC=OB+OC+BC
=7+4
=11cm
If a to the second power plus a minus 1 = 0, find a to the second power plus 1 / 2 of A
a²+a-1=0
Both sides of the equation are divided by A
a+1-1/a=0
a-1/a=-1
a²+1/a²
=(a-1/a)²+2
=(-1)²+2
=1+2
=3
1. Six (1) classrooms are 10 meters long and 8 meters wide. If they are drawn on the school building plan with a scale of 1:500, how many centimeters are the length and width drawn respectively? 2. (1) a part is 10 mm long, The scale of this design drawing is () (2) the total length of Nanjing Yangtze River Bridge is 6700 meters. On the plan with the scale of 1:1000, () cm should be drawn. (3) on the plan of Beijing Metro with the scale of 1:500000, the length of Metro Line 1 is about 10 cm. What is its actual length?
This is the question of new class 32 in Volume 2 of grade 6. If someone has a new lesson, tell me the questions on the next 31 pages,
1.10m=1000cm 8m=800cm
1000 times 1:500 = 2cm long
800 times 1:500 = 1.6cm wide
2.(1)5cm=50mm 50:10=10:1
(2) 6700m = 670000cm 670000 times 1:1000 = 670cm
3.10 times 1:500000 = 5000000cm = 50km
It's not complete. I'm 100% right
The circumference of a rectangle is 242 cm. If its width is increased by 25%, its length is decreased by one seventh, and its circumference is unchanged, the area of the rectangle can be calculated
Width [242 ／ 2 ／ (1-1 / 7) - 242 ／ 2] / [(1 + 25%) / (1-1 / 7) - 1]
=【121×7/6-121】÷【35/24-1】
=121×1/6÷11/24
=121×1/6×24/11
=44 cm
Length 242 △ 2-44 = 121-44 = 77cm
Area 44 × 77 = 3388 square centimeters
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